As others said, depends on the state. Here in CO, ATV/UTVs are not permitted on public roads anywhere (a few areas "look the other way"), even if it's licensed in a state that allows them to be licensed, like UT, WY or SD.
So, for example, my father in law has a RZR that has WY license plates and has all the equipment to be considered street legal in WY. But he can't come down here to CO and drive it on the public road legally. But he can go to UT, where it's also legal, and not have any issues.
Another thing to keep an eye out for is if you need to buy a UTV sticker in the state you're traveling to. We have to when we go up to WY even though we also have a CO one.