I figured the roots would extend into the "material planes", the Fey, Shadow, and Prime planes.
The branches would allow travel to the fantastical outer planes.
In the Norse traditions the three roots of Yggdrasill are "routes", shamanic journey "ways" to the realm of the corpses, the realm of the æsir, and the realm of the jǫtnar.
For D&D, one of the three routes corresponds clearly to Shadowfell. The æsir translate better into D&D "archfey" who have epic levels and who live in the sky of the Feywild. 4e and 5e relocate the Eladrin from the Outer Planes to the Feywild, and any Norse figures within D&D do well to likewise become Fey.
The jǫtnar translate into D&D Elementals and Giants. These are the spirits (minds, souls) of the natural landscapes and waterscapes, including a specific mountain or a specific sea. Their spirit can manifest as if in a humanlike or beastlike form, but they are part of the Material Plane, the actual natural feature itself.
It can make sense to translate the jǫtnar into D&D Giants who roam the landscapes and waterscapes in the Ethereal Plane.
In this case, the three roots have coincidental symmetry with 5e, the Positive, Negative, and mixed frequencies of the Ether, namely Fey, Shadow, and Ethereal, respectively. The roots are natural planar "Crossings".
The animistic view relates entirely to the Material Plane, and nowhere else. So the Ether is always the "Border Ether", never the "Deep Ether". It is always part of and potentially viewable from the Material Plane. For example, the æsir can look down from the clouds of the Fey sky and plainly see Humans in the Material Plain going about their daily activities.
Yggdrasill too is part of the Material Plane. Its crown of branches is the dome of the sky itself, where white claylike clouds fling across it, in the part of structure of the sky that is high above the land. The branches of the sky extend across the world from horizon to horizon.
The trunk of Yggdrasil is the center of the world with the branches and roots extending out from it. Where this center of the world is is unclear. Possibly it was originally understood to be the north pole, with the stars circling around it. But as the known world expanded during the Viking Period, the center of it seems to have drifted southeast, relatively speaking. So by the end of the period, Snorri identifies the city of Troy and the city of Jerusalem, in Asia, as the center of the world.
Perhaps it makes sense to understand the center of the world as each person, subjectively. Around oneself, the horizons form a circle. Then the roots of the tree, can journey from anywhere to anywhere.