My friend died at the scene and the deer had to be "put down", it had broken legs, it happened 4 yrs. ago. Kevin (my friend) was going to work on his Harley dresser when the deer bolted out of the woods.
As for small animals, if you can safely avoid them, do it..but don't risk a crash for a critter. Dogs that chase you are the worse, there are some earlier posts about dogs, search it up.
I had a problem with a neighborhood dog that chased anyone on wheels, I fixed his ass with a water gun filled with ammonia.