As per the myths of the mortal species is all we can say. However, some corroboration from elves, dragons, or other immortal (or nearly so) beings that can/have noted things through the ages is possible.
It is a well known fact by the majority of humans on Orea that Desri, the Grey Lady, elder goddess of death, judgement of souls, fate and prophecy sits upon her throne on the Isle of the Dead (which an island formed of coins, jewels, and grave treasures), weaving her eternal tapestry - every thread weaving the pictorial record of every mortal life -only she knows when that thread ends/should be cut. It is her judgement and unspoken proclamation that sends souls down one fork of the river that brings the souls of the dead to Desri's island/land -on to the bright, peaceful, pleasure-filled upper planes- or the other fork -down the rough rock-filled waters into the dark, fiery, agony-striking lower planes.
In the aged (and declining) "Green Kingdom" of Mostrial, however, Desri is said to exist in an impenetrable spired keep. Passing judgement from her throne. One of the towers of the keep, the "tallest," is an infinite tower, the interior of which is lined with innumerable candles in little niches, nooks, alcoves and shelves. Every flame a mortal soul. Only Desri knows -and/or sends her thunder-ravens- the appropriate moment to snuff out a candle's flame (at that mortal soul's physical death). At which point, the soul will begin to make its way to the Isle of the Dead for their judgement -to eternal rest or strife.
The Gorunduun barbarian clans know, and accept as irrefutable truth, that only the Stone Raven shamans (a clan/order of their own) may speak for or to Charalli, the Stone Raven, Queen of (Noble/Honorable) Death. Her days are spent sending out, receiving, and/or seeing through the eyes of the ravens (rooks, crows, other corvids) that witness and report on the deeds and hearts of all Gorunduun. She then extols their valor/honor or condemns their lack of thereof in life and (particularly) on the battlefield, upon their death. It is Charalli's shrill declarations that inform the collection of other clan totems (the Sky Lion, the River Stag, et al) whether a new soul is to be welcomed into the golden ever-feasting halls of the honorable dead or become [eternal, undying] feed for her (literally) ravenous thunderbirds.
And so it goes for all deities, across various cultures or religions, of Orea (though not necessarily all gods have facets/iterations in all cultures, among all species, or even all communities within a culture.).
Astar, the King of the Gods, the Shining Knight, the North Star, is god of kings, benevolent rule, wisdom (in law and justice), good/just leadership, defense/protection (of your people/lands) against Chaos and Evil, light, good, civilization (in a general sense of community and order). He is essentially thought of as on his throne at nearly all times, at the top the sky (the unwavering northern pole star), overseeing the orderly function of the world/Creation and the forces of Good. He receives reports of the goings-on of mortals (other than his own clerics who are kept up on by his armies of celestial servants, except for the highest leveled priests of his largest temples, with whom he communes directly, on occasion), and any immortals that seek to cause trouble or wreak havoc in the ordered heavens or mortal realms. There's not a lot of freedom or free time for those who would be responsible and good leaders.
Sorilore, the All Knowing, Scribe of the Gods, is generally thought to spend his days recording all history of mortals and immortals alike. He studies and organizes all knowledge, constantly being brought to him by the immortal zepharim (his winged servants/agents). At times, he gazes into his Rainbow Mirror to witness events, in any time or space, himself. These often happen to be pivotal moments/events/decisions for creation. This is all done from his crystalline library upon (or within or hidden behind, depending on the tale being told) Orea's smaller, secondary, green moon. Twice per year, at the green moon's newness, Sorilore weeps and his tears fall to Orea's mortal world. Occasionally those tears fall upon/find a soul and it is those individuals -so it is said- that exhibit the most acute psychic awareness/powers. Hence, the well-known pseudo-religious order of seers (and assorted other psychics) known as "The Emerald Tear" has come to be.
The seasonal deities, clearly have a great deal to do in their certain times of the year. But have three quarters of the year to pursue their own interests/pleasures. The Spring Maiden, Jasralne (Bysdan's twin sister), is also goddess of love, beauty, the visual arts, and dance. So, whether it is spring or not, you can imagine the many enjoyable activities her myths tell of how she spends her time. For the halflings, Jasralne is Jepsabelle, the daughter of their divine matron goddess, a demi-goddess of spring, love, flowers and songbirds. She is "known"/said to spend time -moreso than other deities of any species- appearing in visions and even wandering through halfling communities -in mortal/physical halfling form!- in spring time to bring couples together and rekindle older/lost/forgotten loves (among people, for the arts, pleasure, enjyoment of life, etc...).
Syar, the Stag Lord and Summer Prince, god of untamed Nature (particularly animals) and the Hunt spends most of his time (throughout the year), not surprisingly, hunting. This might be after wicked monsters, unknown horrors or demonic villains, as easily as a particular celestial boar or stag who is challenging/clever/"fun" prey.
While the Twilight Prince, Bysdan, god of music and oration (patron deity of bards), trickery and wit, change and Autumn, is has a rather carefree existence at any time. He is likely to be playing tricks or jokes on his brother Syar or generating mischief for other deities. Bysdan feasts, drinks, and is always up for some love-making with nymphs, fae nobles, or other deities (of any gender). The only real "structure" to his existence is his mandatory attendance to any summons to Astar's court, usually to perform in his role as Minstrel of the Gods.
[might as well round out the year, and gives an example of a -generally thought of as- Evil deity]
Winter is the providence of Wyslia, the Veiled Lady, Queen of Winter, is primarily thought of as goddess of winter, but also goddess of despair, hopelessness, and source/causer of woe and strife. All creatures and hardships of the winter fall under her yoke: starvation, winter predators, illness, deathly cold/freezing conditions, and such are all believed to be Wyslia's pleasurable doing. Stories abound of her schemes against her sibling season deities (or other gods), to usurp their allotted roles, so she may enshroud the world in endless winter. According to those who serve her, and among the farthest northern realms, Wyslia [is believed to] actually "descends" to the mortal plane during the winter months to rule over her season, personally, from a palatial fortress of ice somewhere in the impassable giant lands beyond the top of the world. So, scheming, controlling winter, and creating hardship/strife is what she spends her time doing.
