Your rafters need to be closer together, no more than 2' apart and possibly more like 16-18" (I'd have to look at tables to be sure, and am too lazy at the minute plus about to have to go make dinner, sorry).
You need to make EXTREMELY CERTAIN that the top plate of the walls (at least the high and low ones) are strongly-enough engineered too, b/c remember THEY will be what's carrying the total weight of the roof plus all its snow. If you are wanting to use pallets I would extremely strongly recommend pole-style framing (just using the pallets to fill in the walls) using either 6x6s (pressure treated) if you want to use only corner posts, or a series of 4x4s set all along the wall (again, would have to look up tables for spacing but they'll probably have to be fairly close together.
If you are going with 6x6 corner posts, you will need some really pretty serious beams (the plate at the top of the wall, on which the rafters rest), I live in an area with comparable-or-smaller snowloads and when designing my horse shed, which has 10x12' bays, had to use doubled 2x10s or 2x12s (I forget which) and your span will be longer than mine is so you may have to go to *trebled*. (This gets expensive, and also good exercise to put up there). If you use a bunch of 4x4 posts all along both loadbearing walls, you can get away with less-serious beams, the exact details depending on the spacing of your 4x4s. Consult engineering tables.
Seriously, that is a lot of weight and you need to design for it to be well-supported or you're going to go out there one morning and find your roof caved in on your hens. Do it right the first time
It is certainly very doable, I am not at all trying to be discouraging, it's just important to actually find these things out BEFORE putting anything together
Good luck, have fun,
Pat