Problem: The kitchen is partly over the basement, but also partly in a
wing that includes the garage. The carpeted floor between the outside
wall and the point where the basement starts gets *very* cold in winter.
As a crawlspace there isn't much: 2' perhaps, probably closer to 18". I
have no idea at this point what is under there; the kitchen was built in
the 1970s, but the home dates to 1858.

The carpet needs replacement, badly, and an obvious choice is some sort
of vinyl/laminate.

My question is, are there practical options for insulating *under* the
vinyl flooring? There's already a step up to the kitchen on one side,
and a high threshold wouldn't be out of imagination at the other door.
But perhaps this is a crazy idea. Foamcore-type material would certainly
compress over time and I know that would limit its insulating properties.

If we really had to, and it may be advisable anyway, getting into the
crawlspace while the carpet is up is an option. (No removing kitchen
cabinetry though, so we can't just rip up all the flooring!)

What should I think about in terms of insulating under there, given that
access is such a problem? A vapor barrier is probably code today, right?