If an animal damages your car are you or the park responsible?

You are responsible. It's unlikely though

You assume the risk, but you can rent a car there if you want and it's pretty inexpensive. They won't let you go through in a convertible or a jeep with open sides etc.

You...but they have rentals on hand if concerned

You

Its all on you

You can also rent a bus at their counter and it's not expensive.

The park puts all responsibility on you. They have signs stating enter at your risk.