My son ran over a 4ft garden snake once, he was coming around a turn on a trail and had no time to react other than to scream as he thump-thumped over it. It seemed dazed, but 30sec later it slithered away and didn't seem harmed. And I have a friend that says he runs over rattlesnakes all the time. He says when they're not coiled, they can't strike, so if it's stretched across the trail you got nothing to worry about.

I hit a pigeon on the sidewalk once, in Seattle just north of UW. But it got away, I think I just ran over its tail.

As for deer, just ziptie a rapier to your stem and you'll be fine. Just make sure your rack is rated for 300lb to haul it back and you've got a year's worth of venison!