I don't know how slowly we have to go to avoid running over animals. I ran over an opossum on my bike early one morning. We both made poor judgements on where the other was going, I guess.
One day I ran over a rabbit when I was just running. It came out from hiding by the trail whilst I was in mid-air and I came down on it. I guess if I walked everywhere I could avoid running over things.
As far as I know I didn't kill or even badly hurt the possum or the rabbit, though. They both went running off after the event.