Animations can't change textures on materials. You can work around that by having multiple materials and swapping between them, but that gets annoying real fast.

If we could get a State Machine Behavior like the one mentioned in this stack overflow post [1] it would give some neat new options for avatars.

Links:

[1]: https://answers.unity.com/questions/1253374/is-it-possible-to-change-the-texture-property-of-a.html