You idea for the bucket loader shovel out is good.
I understand your barn configuration now and agree the hardware cloth is also needed.
Here in Colorado we can get deep snows and temps well below zero. In the winter I only keep them cooped up if the wind is whipping and we are below 20 for the high. I have to shovel the run and I did put a "roof" on one end so they always have a dry and or shady spot.
I know you get more snow then we usually do but thought the info may be useful. Oh and I do not heat my coop.