You would have to check with your local ordinances and zoning laws but as long as the town allows travel trailers or mobile homes then you can legally park either one on someone else's property if they allow you too.
But you should always check with the local zoning laws and ordinances to be sure otherwise they might give you a fine and a warning to move it off the property.
If you live out in the countryside or in the woods then it's likely okay as there's really no zoning laws or ordinances when it comes to living out in the countryside away from neighbors.
If you're in town or the city then living in a travel trailer may or may not be legal but at first you'll probably get a warning if it's illegal and be given enough time to move it.
But checking with the town would be a good idea first.