My cousin bought a cargo trailer and set it up as you are thinking. One major issue is the trailers are metal which conducts heat/cold well so their trailer gets really cold in the night, not any better than a tent. Your going to have to insulate it well.
The other issue is the maintenance and storage of a trailer. Do you have a place to store it, if your in a city chances are you can't in your yard so it will have to go in storage. You also may need to worry about dry rot on the tires, rust on the brakes, winterizing the plumbing, etc. Then there is the state licensing fees and such.
I picked up an old truck camper for $600 and am rebuilding it. The popup top makes it small enough to fit in my garage where I keep it plugged in and ready to go. In most states a truck camper doesn't need licensed since its 'cargo' and since no tires or anything there isn't any maintenance like a trailer.