It'd be cool to see animals having to rest after reaching below a certain stamina point.
If this isn't too tough to code I think it's a neat small feature you could add in. Give them a lot more stamina than 100 running and 90 fortitude though.
Also, it'd be nice if deer ran faster than human sprint when running away from someone. To hunt deer and other fast animals who are terrified of humans, you would have to be an archer, just like real life (or rifle).