Placing the coop under a shelter will prevent snow blocking the door and rain or snow entering the door, windows and vents.Attaching a tarp over it is all you'd need.
We had chickens when I was growing up but ours roosted in trees.I made the same mistake with my first coop too but after I was told about the need for ventilation I corrected the problem by raising my roof 2 feet.I tore my rafters down,made the sides taller and designed my roof to have an overhang.