Missoula has average lows below freezing October through April, average highs below freezing December through February. Elevation in the valley is about 3200 feet, rising to about 5000 in the surrounding mountains. Winter is fairly dry, averaging less than 40 inches a year, but accumulating most of that during the three months it stays too cold for snow to melt.
Wintering there will be an interesting experience for someone from the coastal plains of South Texas. I have family west of Missoula, ranching in the mountains, and friends in Billings, urban lifestyle. These people like it there, having either lived their whole life in the Rockies or moved there from parts of the Midwest with similar, maybe slightly warmer and wetter, winters.
Strategies for coping with the winter weather include enjoying it, with active outdoor winter sports, and hunkering down in their well insulated, well warmed homes. Having at least one room overheated by a wood fire is often part of that. Living like this might encourage someone to stay.
Living in a mobile home in a trailer park, living in a RV adapted to perform something like a mobile home, are both doable. Some RVs will be better at this than others. I would not try it in mine, I know how cold the walls and windows get in weather just close to freezing, and there is not enough heating to overcome that. But others do better.
The RV or trailer park life will be more like a survival mode. I would not make that part of the "adapting to Rocky Mountain winter" experience if I wanted the person to decide to stay. But I have friends who lived in Anchorage, in a trailer, and they stayed at least 20 years. But maybe Anchorage is not as cold as Missoula, though definitely wetter.