I think its is possible to use rammed earth still. They use it in New Mexico where it is cold and snows.
You want to avoid snow drifts from piling up against the walls because that will inundate the walls with moisture and weaken the rammed earth.
Also a high concrete foundation might help as well, maybe 18"+ inches above the ground instead of the standard 8"

Some large overhangs over the rammed earth can help keep the walls dry and prevent snow from sitting atop the walls and slowly dripping down.

For the winder try to calculate the roof overhangs so you still get winter sun into the home, but summer sun out.

What part of the country is this in?

Rigid insulation rammed in the walls. Plently of rammed earth in cold Canada.