When you know you’ve had enough.
You go out for a few drinks with your friends, not trying to over due it, then, BAM!! Next thing you know you’ve flopped out of your little tree bar and now hopping around in the snow like the Easter bunny, trying to figure out which way up. The trees are no longer straight and the smallest snow piles now seem as big as the rocky mountains.
So to answer the original question, yes, animals can get drunk. Even naturally in the wild it can happen. When fruit falls from the trees it begins to rot and ferment. When animals consume the fermented fruit, the inevitable will happen. Just watch this squirrel doing the walk of shame after an all night crab apple binge.