Lots of folks in my area have permanently set up travel trailers as summer cabins, and snow is an issue here, too. One common solution is to build a snow roof over the trailer. Some parks allow it; others don't.
Arizona separates ownership (title) from
registration (for highway use). When I lived in a TT full time I got the
title in my name and filled out some papers assuring the motor vehicle department I would never pull the trailer on a public highway instead of
registration. It's been over 30 years ago, so my memory is a little foggy, but I think I had to arrange an on-site
VIN check by a law enforcement officer in lieu of bringing the trailer to the motor vehicle office.
Different jurisdictions, different rules, but since it's a common practice you can bet there's a way. You are on the right track talking to motor vehicle departments on both ends.