One of the first roadblocks I see in the making of a tiny moveable house is the trailer. What kind do you use? The standard a-la-tumbleweed seems to be a sturdy duel axle trailer. Almost every tiny house build I've looked at seems to use one.
They are, however, expensive. Even used ones on craigslist are usually well over $2000.
There are those who have bought an old decrepit camping trailer, demolished it, and salvaged the underlying trailer, but that's a lot of work... and craigslist says that people selling old decrepit camping trailers still want good money for them.
My father thinks he could build a small house much lighter, so light that it could use a single axle... and those do seem to run a bit cheaper. Another thought he had was to build one on a trailer made out of an old truck bed like so.
My first thought with that plan is that truck beds are quite small, though I have found myself evaluating them more shrewdly as I pass them driving around, and some of the older ones are quite roomy.
Another problem could be the height. Most trucks seem to be higher than most trailers, and since you can only go up to 13ft (I think) and be road legal, and since the lower you are the better I imagine your aerodynamics would be, it could be a real problem to be starting so high up. The height could also be a problem if you planned on towing it with a car.
Still, if searching the local craigslists and newspapers and putting in a word with the local mechanics and junk yards didn't turn up a usable trailer at the right price, it might be worth asking the local mechanics and junk yards how much they would charge for a truck bed trailer.
If nothing else, it would at least make for a very unique tiny house build.