Thing is, if a tiny house is on wheels, and is registered as a trailer, HUD and the building department have no jurisdiction as it's technically not a house, its a vehicle. Where you park it might get zoning involved, but that's it. The same applies to vans, motorhomes, travel trailers, etc. The HUD regulations apply to "mobile homes" which are manufactured as housing and not intended to be moved often, if at all once set up.
You might look to RVIA for recreational vehicle standards, but RVIA is strictly a voluntary industry organization, not a government agency. Tumbleweed Tiny homes, for one has gone the RVIA certification route, and they are at the forefront of the push for having all tiny home manufactures work toward some standard. I have mixed feelings about that. It does help to legitimize the movement, which can help more communities be more accepting of them. But it will also drive up the costs defeating one of the primary original goals of providing alternative housing that is more economically and environmentally responsible. Similar goals to why many people become van dwellers.