Not sure about mice but my rats do. It’s more a occasional
treat, as some rats can be lactose intolerant, and there’s nothing fun about cleaning a cage after you’ve given a LI. rat dairy.
You see rodents on cheese in cartoons because rodents were a big problem for people trying to store cheese in cellars. It’s not that rodents love cheese, it’s that they’ll eat it and people used to store cheese in prime rodent habitat.