These are two very different things. Beware the difference.
Longjohns or thermal longs put an insulation layer over your legs. In cold weather this can help keep both your feet and your whole body warm. And yes, I have seen people walking with thermal longs and shorts. I have worn them myself in the winter. They work, but watch out for the scrub.
Compression tights are not designed for warmth but to compress your legs. In doing so they restrict the flow of blood down and up your legs, with three consequences:
* your leg muscles are starved for energy because of the restricted blood flow
* your legs and feet get cold because of the restricted blood flow
* you enrich the vendors
Yes, I know they are heavily advertised with all sorts of medically false claims, but so are cigarettes and crystal healing. Yes, I have tried them myself, with bad results. I even tested them while sleeping, but my legs froze (so I took them off and was OK).