I've been thinking about this topic myself recently. Going with or without a car is obviously going to depend on many variables. For example, it might serve you well to go without a car in an area with a mild climate, school and food store nearby where you live, etc. - you could probably get by with a bike or a scooter. In an area with a cold climate, however, you might want to re-think about having to bike or take a scooter to school/food store/etc. during the winter! I suppose you could always ask a friend who has a car to take you somewhere when it's snowing or whatnot, but that might be burdensome. Or taking public transportation, like you mentioned, could be useful when the weather is sour and you need to get somewhere.
I personally think going without a car in vet school would be a great idea if it's feasible! 👍 I don't know how feasible it will be for me, though, if I get in to Iowa... but I'd like to think I could make it work!