There's no inherent reason why they couldn't be registered and towed about. Depending on the state laws and how they are outfitted, it may not be possible to register all of them as RVs, but an ordinary trailer registration should still apply provided the appropriate safety and other DOT regulations (height, width, etc.) are adhered to. In many cases, if not an RV, this would be a sufficiently large trailer to need a CDL.
An RV, as opposed to a general truck or trailer, is legally defined in most places as having at least a certain number of certain living quarters types of facilities: a bed, a toilet with a holding tank, a sink with running water, an installed electrical system, a furnace, a cooktop, etc. The specific requirements do vary from state to state. Any vehicle or trailer that meets these requirements may be registered as an RV.
Many of the tiny homes I've seen information on are not really designed for continuous travel, but instead more of a transportable shelter—closer to a park model RV or small mobile home than a travel trailer.