Hello, I was stationed in Minot a few years ago, so I know where you are coming from. I recall it snowing as late as May 10th, craziness!
Are your chicks from last year now a grown flock?
Best might be to put fertile eggs under a broody hen. Then she could just raise them in the coop. But, if you don't want to do that or don't think you will have a broody hen soon...
At 4 weeks I would think they would be old enough to cuddle with your older hens, so long as they are not getting attacked too much. Maybe you could start introducing during the day time at the beginning of the 3rd week?
No garage, basement, or shed w/electric to let them get to 6 weeks huh? rough. Maybe a neighbor could house them for a bit in one of those places? You could offer some of the future eggs in exchange.
I think if you got them May 1st it might work? The couple years I was there it was warmish by the 3rd week of May.
What about a local farmer? They might want chickens too and have space for them, you might work something out.
Otherwise buying a point of lay pullet might be another good option.