In the US, the semi-movable structures that are intended to be more or less permanently placed for living are generally called "trailer houses." Those intended to be regularly moved about get a variety of names, like "campers," "travel trailers," or even "house trailers."

Most communities in the US have one or a few "trailer parks" where people have a "trailer house" moved in and anchored to at least a partial foundation. The "foundation" in this case often resembles a set of jack-stands or an assortment of concrete blocks, but often there's at least a slab of concrete, electrical hookup, and a sewer connection. Most use propane for heat and cooking. Usually wheels and axles are removed and sent back to the factory; or they're owned and kept by the guys you hire to move it for you. You commonly have to sign at least a one year lease for the lot, and pay monthly rent. Some places require rather longer leases - up to 10 years, I've heard.

In most places where these "parks" are found, there are mandatory requirements for anchoring the "trailer" to the foundation, and most places require "skirting" to close the gap under the trailer. The skirting does help a lot in keeping a strong wind from lifting the trailer and turning it over, so it's not just to keep the pipes from freezing. Wiring in these is nearly always straight 110V AC, the same is in permanent houses.

In my area, the "anchoring" that's required is largely so that when the tornado takes the trailer away, it also takes all the loose pieces of foundation along as well, leaving a nice clean slab for the next victi.. occupant.

Double-wides are quite popular, where two trailers are parked side-by-side and bolted together. You can assemble a 20 x 60+ foot "house" this way.

Places where you can rent space intended for campers, travel trailers, or house trailers - what's being called caravans - generally are called "RV Parks" here, even if residents are mostly fairly permanent. In many parts of the US its possible to find a year-round RV Park, but until you've confirmed that there is one available at your destination you probably shouldn't depend on it. The majority of RV Parks shut down in the coldest part of the winter, and in whatever they consider their "off season."

Zoning and construction restrictions prevent you from putting a "temporary" structure, trailer or otherwise, on your property and actually living in it in many cities and towns, and in some fairly rural areas; but in quite a few places it's possible to set one up if you get far enough out of town. Quite a few farmsteads in my vicinity have a crumbling abandoned old farmhouse in front with a trailer "in the back yard" that's the actual residence now.

John