During the Viking Period, the Norse normally avoid wearing fur. The reason appears to be, according to custom, only the Vǫlva shaman wears furs. Fur is a sacred clothing, and signifies a sacred institution.
Indeed, the Norse even make fake fur. The fabric for this ‘fake-fur cloak’, vararfeldr, is a pile weave, where uneven wool hairs are woven into the fabric with both ends facing out to resemble fur. The cloak is labor-intensive to produce and popular for winter wear. In Ísland the fake-fur cloak becomes legal tender, and in the context of using the cloak as money, sets the standard size of a feldr ‘cloak’ to be about 1 meter by 2 meters.
Archeologically, fragments of such cloaks survive. The wool can be died for any color. There is even mention of a cloak woven to produce striped fake-fur. A unique instance of a Saxon wrap jacket dyes the fake fur pink for the trim of the jacket (with alizarin acid from madder). Shaggy fake-fur cloaks are also popular in Írland.

Ragnarr Loðbrók (one of the heroes of the tv series, Vikings), his nickname Loðbrók means ‘wool-tuft pants’, from lagðr ‘wool tuft’ and brók ‘pants’. Presumably his fake-fur pants are for winter. But the Norse thought the use of this fabric for pants was unusual enough to earn him a permanent nickname.
Here is an image from the Torlunda bronze plates from the 500s-600s (discovered in today Sweden). Altho before the Viking Period, the man appears to wear the loðbrók wool-tuft pants. He leashes an animal (probably a large wolf with ears and tail) with one hand and holds an axe with the other. These bronze plates are thought to depict a ceremony.

Archeologically, the only example of fur clothing that I am aware of is a fragment of a fur-trim hat in Svíþjóð (in the town of today Birka). But it is in the context of the Garðariki clothing styles, and here this Proto-Russian ‘gerzkr’ hat is of a style still in use in Russia today. The wool ski hat closely fits the head, with fur lining around it. It might be a souvenir from a business trip abroad along the riverroutes.
Noregr also knows about the fur garments that the arctic Finnar wear (today Sámi). The annals of King Alfred (of Anglo-Saxon Wessex) record an account about Ottar from Hálogaland, who brought fur skins from the Finnar including reindeer, bear, seal, otter, marten, and a cloak of bear fur.
An Arabic account in Serkland (relating to Bagdad) mentions Norse merchants themselves supplying the furs of marten, fox, steppe-fox, beaver, hare, and goat.
The Norse are hunters. Furs are abundantly available.
Norse texts know about garments made out of fur skins. The notable absence of fur garments in archeological contexts surprises me. This requires explanation. Fur is an issue that I am still looking into. The following is my current impression.
So, furs are everywhere. Why arent more Norse wearing them?
A look at the Norse texts suggests only the Vǫlva shamans wear furs. Fur clothing appears to be the sacred ceremonial garb signifying a Vǫlva. By extension, informally, laypersons who demonstrate shamanic powers might also wear furs.
For example, one saga specifies how a Vǫlva shaman, Þorbjǫrg Lítilvǫlva, wears a hǫttr hood made out of black lamb-fur, and lined inside with cat fur. Additionally, she wears shaggy calf-fur shoes, and cat-fur mittens. The text’s attention to her garments of fur attests to their being unusual and significant.
An other saga uses the expression, ‘waving a goat fur hood around our head’, to mean inducing mind-magic illusions, literally meaning that such a heðinn fur hood is used in this way. In this saga, the mind-mage employs her magic without actually waving any fur, yet the traditional connotation of fur skins here is telling. Other sagas also mention wrapping a fur hood around the head of the shaman or around the head of the target to induce illusions.
Where Þorbjǫrg is a human Vǫlva, Freyja is a vanir Vǫlva. She uses a cloak of falcon feathers for her shamanic magic to shapeshift into a falcon, the feat of a particularly powerful shaman.
Here is an image of an inline fur hood, suggestive of the one that the shaman Þorbjǫrg wore. (It might help to translate the word hǫttr ‘hood’ as ‘poncho’. I modified the original image for a more angular front and a longsleeve dress).
Relating to the feminine Vǫlva, the berserkar employ a masculine use of shamanic magic, allowing for courageous personal combat. The berserkr shapeshifts ones own mind into that of a dangerous animal, and sometimes the body too.
The nickname ‘bera serkr’ literally means ‘she-bear dress’. Notably bera is a female bear, and serkr is the dress that women wear. The only difference between a mens tunic (kyrtill) and a womens dress (serkr) is the length, thigh-length and ankle-length, respectively. And the womens outer dress with the shoulder straps can be calf-length. Thus a garment whose hem is below the knees can appear gender-ambiguous.
When looking in the origins of this nickname, the animal fur of the berserkr seems to derive directly from the Finnar shamans (today the Sámi Noaidi). During the Viking Period, the Finnar clothing styles include a mens outer tunic that is long, reaching below the knees. For the Norse whose tunic is thigh-length (anywhere from groin to above knees), the calf-length Finnar tunic below the knees can resemble a Norse dress. So the name ‘serkr’ appears to refer to a Finnish mens tunic.
Finnar typically wear wool, but are also known to wear garments made out of fur, including bear fur. Thus the ‘bera’ of ‘bera serkr’ likewise appears to refer to a Finnish mens tunic that is made out of bear fur.
Nicknames are nicknames, sometimes ironic. For the Norse, to refer to a shamanic warrior as a ‘bera serkr’, wearing a ‘dress’, probably connotes how, for Norse custom, only the Vǫlva shaman wears fur, and only a woman can function formally as a Vǫlva. At the same time, the ‘she-bear’ connotes strength, power, and maternal ferocity. They respect the berserkr as a deadly warrior.
Here are images of an arctic Finnar tunic from about 1000, discovered well-preserved in the today town of Skjoldehamn, in northern Norway. It is actually wool woven with colorful patterns, but here its brown from aging helps visualize a bear fur. His DNA matching that of the Sámi confirms his identity as Finnr. Note the calf-length of this tunic reaching below the knees. To the Norse this can connote a Norse dress. Also note the distinctive widening skirt, for full maneuverability of legs.
One saga reports a Finnr (a Sámi Noaidi shaman) using reindeer fur for combat clothing. They esteemed it to be even more effective against weapons than metal chain armor.
‘ Þórir Hundr had many kinds of dealings with the Finnar. There, he had ·them· make twelve reindeer fur-tunics, charged with so great a multitudinous knowledge ·of diverse kinds of shamanic magic· that no weapon could penetrate them. ’
The text seems to describe an indigenous Finnar example that relates to the Norse berserkr magic. Note, this term ‘multitudinous knowledge’ fjǫlkynngi refers to a shaman who is skilled at different kinds of magic, such as prophecy, mind magic, shapeshifting, outofbody projection, teleporting, and so on. The reindeer bjálfi fur-tunic can transmit the mental power of the shaman. The Finnar shamans employed magic for combat, in a way that the Norse considered reasonably masculine, in this case, because it is for defensive purposes rather than an unfair attack from the distance, and allows for courageous personal combat.
The nickname ‘she-bear dress’ likely originates from a similar Finnar long tunic made out of bear fur.
Note, the nickname ‘berserkr’ originates from the use of a distinctive bear-fur long tunic. However, the Norse berserkar shamanic tradition came to employ various other kind of furs in the shape of other kinds of garments as well.
A fur in itself can imbue the wild mindset of an animal. One saga mentions a traveler coming across a berserkar campsite while the berserkar were currently on a wolf-shape run. The traveler put on the wolf furs to keep warm by the fire, and accidentally became overwhelmed by the shamanic shapeshifting magic, transformed into a wolf, and went on a bloodthirsty frenzy.
The Norse perceive the berserkar as wild, ferocious, antisocial, magical, and dangerous. Essentially, they are shamanic gangsters. There is a kind of love-hate fascination with them.
One saga (Grettis Ásmundarsonar) mentions King Haraldr in Rogaland (in today Norway) shrewdly employing berserkar as personal bodyguards. They were famously nicknamed the ‘wolf fur hoods’ (úlfheðnar). ‘They were called wolf fur hoods, but no iron would bite on them.’ (Þeir voru kallaðir úlfhéðnar en á þá bitu engi járn.) Despite their vulnerable armorless appearance, clad only in fur, they prove invulnerable to even metal weapons. Other sagas likewise mention these ‘wolf fur hood’ berserkar (Haralds Hins Hárfagra, Vatnsdæla, Hrafnsmál). Again, this term ‘fur hood’ ostensibly refers to the connotation of a Vǫlva wrapping a fur hood to transmit a magical effect.
The form of these wolf fur hood appears to be identical with the kinds of fur hood that some of the Vǫlva wear. Pop culture tends to portray the berserkar wearing a raw wolf pelt with the wolf head still intact. Nevertheless all known examples of shamanic furs are well-crafted garments. In any case, the Norse observers understood the magical nature of these warriors − because they wore fur.
Keep in mind, the Norse wear leather shoes and leather belts. So, specifically the fur seems to connote the ceremonial shamanic garb.
In sum, for the Norse, fur clothing seems to represent a separation between the human social order and the shamanic magical wilderness. The Norse can and do sometimes wear fur clothing. But it is sacred and dangerous, and never done carelessly.
If Norse individuals wear a fur garment, likely they are displaying their skill in shamanic powers.