Yes it's legal to live full time in a camper trailer or travel trailer or even motorhome.
However while it's legal to live in a camper trailer, travel trailer or motorhome it may not be legal to live full time in one spot such as in a town, city etc.
Check with your local zoning ordinances as some cities and towns prohibits the living full time in a camper trailer or motorhome on your property.
But if you have a place that is rural then you could legally live full time in the camper without any issues.
You can also live full time in your camper or travel trailer or motorhome while traveling on the road.
A lot of people live full time in a camper trailer, motorhome and then travel from state to state and it's legal to do so.