So, at this point Bears, and Spiders have "combo" abilities that can cause additional damage to players via trapping them and causing reel, and then exploiting that. In that light, other animals should maybe have some additional mechanics/abilities that are similar. Say, with Deer, when they charge you, it would basically be like a Bullrun, and stun you if they hit you. Besides that, they might also have a "reer" attack in which they use their front hooves to hit you, and this would do more damage if you were stunned/reeling from the charge. This would reward avoiding the charge.
March Hares might also have more moves, including a "leap at" like attack, (Reminiscent of the Killer Rabbit, logical for a rabbit, also makes them more dangerous because they would be able to unpredictably close distance on you very quickly.) They might also have a "kick" type attack similar to leg sweep that would work about the same (Making it harder to escape from them, and generally kite them as you can now.) It would make sense since rabbits are big on kicking things when they defend themselves. (You could also have the "Kick" be like an uppercut, or give them another kick variant that was like that, besides the "Sweep" style one.)