You'll need an engineer for this. Wind load is going to determine the design. Canopy wind loads fall under 30.11 from ASCE 7-16. Once you have a wind psf, then IRC tables can provide your framing sizes, where you could substitute 0.75(20psf)+0.75(0.6)(wind psf) for the tabulated snow psf.

My wild guess is that a 10 psf dead load plus 30 psf snow load under IRC rafter tables provides sufficient framing for your patio cover. 10 psf dead load plus 40 psf live load under IRC R507 should yield a conservative design.

You'll probably need a load path down to the foundation for resisting uplift, too. Typical deck details will get you 90% there (toe nails in joist hangers and notched post connections with 2 bolts each), but the post bases will probably need some tension detailing.