woodchopper: my cat has sentimental value to me, far above the monetary value of a horse.
Something runs into the road, and it's a natural reaction to hit the brakes, not matter what it is.
However, given enough time to think, if it were likely to cause an accident that would result in injury to another person, I would ease off the brakes. Sorry, pussy, or doggy.
Badgers do wreck your car, I've seen it! Catch a fox wrong and it's nearly as bad. A long time ago, I knew a lorry driver who had a deer run into the road in front of him, in the New Forest. Made a right mess of the truck, though fortunately he wasn't hurt.