We know what you're probably thinking. There's a lot of deer talk in As You Like It and it's not always about sex.
For example, when Jaques goes on and on about a wounded deer he watched crying big, giant tears into the river, it seems to be more about social injustice than cuckoldry. The evidence? Well, Jaques says deer hunters are "usurpers" and "tyrants" who scare the poor animals and kill them on their home turf (2.1.2). Even Duke Senior says he feels bad about killing "the poor dappled fools,/ Being native burghers of this desert city" (2.1.1). The idea here is that the deer are the original citizens ("native burghers") of the forest and the Duke's men have come in and taken over their space. Kind of like the way Duke Frederick usurped his older brother's title and dukedom, right?
(By the way, when someone talks about an animal or an inanimate object as if it has human characteristics, it's called "anthropomorphism.")
Literary scholar Katharine Eisaman Maus says that deer hunting is also associated with "resistance to tyranny" in As You Like It. In Shakespeare's day, the forests of England (and all the deer in them) were the property of the king, which meant that killing the king's deer was a big no-no. Yet, for the poor who couldn't afford to go out and buy food or couldn't grow their own, deer-poaching was a way to put food on the table...and to defy the king.
So, when the exiled Duke Senior hunts in the Forest of Arden, he's associated with outlaw behavior (like poaching deer) and becomes a Robin Hood-type figure who runs around flipping the bird at authority figures – namely, his evil brother, Duke Frederick.