We have lots of rain but as per the snow load it's never more than a few inches (6-10 max), I wouldn't mind going out in the middle of the storm to shovel the coop. We don't have more than 3-4 big storms in my area (this past winter we had only 1), and I love being outside when we do. I was planning to put a few 2 x 4s to hold/screw either the hardware cloth or a solid roof, so I don't think that would be a problem as per snow load rates.
This is something I will keep in mind, I guess it's the best bet to ditch the pallets and build the apron. We don't really have big snakes, and it's only a problem from June-August since our temps are not as warm as these guys like. As per mice I guess they could be there year round but not sure they can grow to a big size to pose a threat to chickens?
Thanks for everyone input so far!