Not just the rafters. The wall construction of the run was not designed to carry a lot of load. The spacing between studs is not sufficient to support the top plate with rafters and roofing with a high live load. If the spacing is maintained then the top plate needs a beam and the 2x4's need to be doubled up. And the load needs to be carried to firm ground that will not heave during the winter freeze/thaw cycle. That means footers dug to below the area frost depth. The OP is in Southern NY. I am in Southern NY. My code depth is 42".
The bare minimum pitch for solid metal roof 2/12. More is better as it will hasten the drainage of rain and snow from the roof.
Excellent points! I hadn't even looked at the walls or ground posts. Now I understand why you said 2/12...it's for a solid sheet! Everything I've been reading has been for the ~3-4' wide sheets which overlap, and everything says 4/12. So many variables!!