For specific examples, we look at a round-up posted by user "Kimmeruwp." According to Kimme, after mastering level 1 of Squirrels (presumably Brown Squirrels), they all vanished. For another farmer, after reaching level two of the original Horse mastery, all of those animals vanished as well upon refreshing the game.
Now, I hate to alarm anyone, especially when there aren't many other claims (as of this writing) of issues occurring, but as this was just reported within the last few minutes, I find myself erring on the side of caution. It isn't impossible or even unlikely that Animal Mastery has been released with bugs in tow (this is Zynga, after all), so if I were you, I'd keep an extra eye on all of your animals, especially if you're about to hit that next mastery star. At the very least, take the extra time to manually harvest each animal, rather than using a Farmhand, and keep refreshing while doing so, just to keep an eye on things. Better safe than sorry, right? We'll make sure to let you know if this does become a larger issue, or if it remains isolated.
Have you had any animals disappear while trying to master them on your farm(s)? Sound off in the comments.