Well, in fairness Tumbleweed Homes are premium. I'm just giving a starting link as a hint. If you're looking for serious cheap & portable along those lines, I got a used pop-up camper for $2000 (new $10,000) that I'd be OK living in (and do for a few weeks a year, family of 4 + 2 dogs). During a sale, I also got the detailed plans for a Tumbleweed Home for $20, simple enough one could scrounge most of the materials. You can spend as little as you like, so long as you're willing to DIY and have flexible standards.

Speaking of which... Go to the Zillow link and search (largest range allowed is a whole state) for properties at/under $1000. Dig thru the auctions/scams/typos, and you'll find viable - even nice - lots dirt cheap.

Put those together, deal with misc paperwork & other costs, be ready to work, and you can have a home free-and-clear for under $5000. (Yes, it's not a 2400 sq ft ranch in the suburbs; deal with it.)

I've found the tiny-house movement fascinating to watch from the outside. It's got a real appeal to me that's only increased as I've gradually transitioned from my youthful can't-wait-to-be-uploaded outlook to a much more reluctant relationship with tech and the always-on life.

My concerns about trying it myself:

1) The country-living variety defeats any small-ecological-footprint appeal, unless you live like depression-era or earlier farmers (i.e. don't underestimate the ecological sensibility of a studio apartment in the city)

2) The urban/suburban variety is much harder to make work if you don't want to live illegally in someone's backyard, thanks to zoning, HOAs, et c., plus the cost of land very nearly ruins the money-saving angle.

3) Health care is really, really expensive. I doubt I could make enough money to cover that for my family, on top of other unavoidable expenses, while living a disconnected life in the sticks, as much as it might appeal to me otherwise, even with the savings from not having rent or a mortgage. That goes beyond "roughing it" to "irresponsible".

4) I've got a tickle in the back of my mind that a large part of this is a marketing ploy to sell mobile homes at a premium by appealing to "economy" and "eco-consciousness" when both of those would be better (or at least similarly-well) served by buying single-wide in an ordinary mobile home park, which for some reason[1] rarely comes up as an alternative. Incidentally, if you've ever been to poor rural areas along sleepy back-woods highways, you've undoubtably noticed that you can do the trailer thing and the dirt-cheap-land middle-of-nowhere thing, too. Of course, they're ugly and couldn't possibly be mistaken for Thoreau's cabin.

Your pop-up camper approach seems sensible (though I, also with a family of four, can't imagine living quite that small full-time without going insane—a few weeks a year, sure) but it's not the kind of thing you see blog posts gushing about, covered by documentaries, or featured on magazine covers.

[1] Class, almost certainly; trailer park = white trash redneck, "tiny house" = creative class, educated.