Zero F isn't particularly cold (as chickens account such things, anyways). 64 sq ft is tight but potentially doable. More so if its an 8x8 square which will help keep one dominant bird from controlling the whole space.
8x12 or 10x10 would be much better.
The "thumb rules" as a starting place in your design are at least 4 sq ft of house and 10 sq ft of run for each bird, exculding space taken by nesting boxes, food, water, etc. Plus 1 linear foot of roost and 1 sq ft of 24/7/365 free ventilation per bird. Using an open air coop design (basically, covered on one side plus half of two others, with the "back" pointed in to the prevailing winter winds) can help you cheat a bit on the total area requirements by blending "coop" and "run" into a single space.
The time to ensure you have good drainage is before you erect the coop, and the design of your roof is dependent on your snow loads - but you should include big overhangs regardless, they help in a lot of ways.
And two nesting boxes will adequately serve 6 hens. Three if you are feeling very generous.
I threw together an 8x12 hoop-coop style tractor a couple weekends back for a few hundred $ I use as a grow out pen for the latest hatch. Its 96 sq ft and is roomy for four baby ducks. Its adequate for six full sized hens, or as a place for the four baby turkeys going in it next week while they get some size on them.
Most people would consider it big enough for six adult hens, but I free range on many acres, so I am a poor judge of such things.
