The quintessential bugout solution is not published.

During the Great Depression, many people built survival shelters in the ground. They did precisely what Civil War soldiers did during Winter.

Like this:
[link to t0.gstatic.com]

or this:
[link to www.coyotetrails.org]

or this:
[link to www.coyotetrails.org]

If you had to bug out, could find a quiet place near water and a meadow (clearing for growing crops) and near forest, but with an overhang of earth (hill-side) then you could dig in, build a frame, clear it out, and make a hobbit hole. It wouldn't be perfect, but pretty warm.

If you can go down a bit, you in essence built a root cellar.
[link to www.anr.state.vt.us]

It will stay warm to 50 deg F. That means FAR LESS fuel to heat it. Most likely wood, but if lucky enough to be near a cow pasture, then you could burn dried cow manure like your ancestors would have done.

It will be naturally cool in the heat of Summer.

I reckon a lot of folks could head to the National Forests and do just fine as long as they had some common sense and a whole lot of fortitude.