I've lived in Canada and now the Midwest where snow can get good depth at either place. We've always used tarp reinforced with additional cross beams and tied with hard ties, but some off the shelf walmart tarp won't cut it. You need "heavy duty" tarp rated for all-weather use. You can generally expect reliability out of it for around 10 years.
We tried the corrugated roofing and noticed three things that made us switch. On the rainy days the sound it makes drove both the animals and ourselves nuts. When it hails, they get beat up really quick and easy. especially if they have a couple years on them and have gotten brittle in the case of the plastic types...and on the windy days, it becomes a great big sail that can really put some test to your anchors if they aren't rock solid. Where as the tarps somehow seem to have more "give" to them.
Anyway, it will all come down to what you're dealing with in your particular area and the type of weather. I would ask a neighbor or buddy to see what's worked best for them.