I have worked more than one wreck where someone, usually city folks, rolled their high dollar cars, endangering their entire family, for critters, usually something like a coyote. One of the last I worked put her car upside down in a waterfilled centerdivider, almost drowning herself and her son, to miss a jack rabbit! (which she hit and killed anyway). Long legged critters, such as deer, elk, moose, horse, you don't want to hit, they will usually slide over your hood and come right in thru the windshield. Really heavy critters, such as cows ('specially bulls), are to be avoided also. But smaller critters, hit them, your family is more important...
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OBG