There are way too many governmental jurisdictions to make broad generalizations. Everything from no camping except in designated areas and limitations on firearms to camp just about anywhere you want.
I doubt there is anywhere on public land you can just build a cabin though. I get the impression you might be thinking you will live off the land; those days are long gone.
I'd say you need to do a lot more homework; there is a vast amount of data on the net. For example, have you looked at the temperatures in Yellowstone Park in March as a starting point?