PS: if Haut "cutis, skin" and Haus "house, family, sex" ("race"?) share a root, is that a remnant of racism? Scandalous!
No, because even if they did share a connection related to "skin", there are far simpler speculative explanations, like animal skin being used as a covering for a tent like house structure, like on a yurt.
A Scheuerlappen, "rag cloth" like a burlap, might be out of leather, though usually of rather coarser material. Just saying so because yurt (from mongolic) reminds of shirt, skirt and Schürze, in rhyme. However the r implies another root, "to cut", same as for Geschir "cutlery, dishes; harness [of horses]; vessel" (though zurren, zerren "to strap, stretch" might be akin, also see zieren, too).
I don't think your notion is implausible, but we have the words tent and Zelt already, and howmany more. housing in that sense, as something movable, could be paradox for a immobilia, but who knows.
While "to hide, conceal" might explain the connection reasonably (note that hide~leather is related closer to Haut than hiding), that would have to be the connection to rule out all others, but it's not that simple. Many \ske- roots relate to "to cut", and in my mind many figurative idioms can be derived from that sense to explain this or that. On the other hand, s-mobile may be treated as a prefix, and, assuming the prefix was sek- originally (i.e. "off"?), then we are left with a load of short stems -et, -es, .... Which reminds of some Akkadian words, and the question about who invented the se-dentry life style.