I've wondered about this too. I have seen ungulates standing belly deep in a pool of water in zoos, presumably to cool off, and some terrestrial species like to play or stand in water more than others. But purposely going into deeper water and swimming around aimlessly the way they often do in game seems strange.
I did find this website, claiming that zebras will swim for fun and can actually defend themselves from crocodiles, even when swimming, but there are no references provided.
Swimming for Zebras? There is a lot of confusion surrounding this as people want to know whether Zebras can swim or not. Many people restrict swimming to
equinedesire.com
I agree it would be fun if animals could have personalities in the game. It's certainly true that some members of a given species, or even specific breed with domestic animals, enjoy playing in water more than others (I've had two Australian kelpie dogs, and one wouldn't even get his feet wet at the river, and the other dives right in) and have many other preferences and quirks too.