The manual said it was designed to handle snow loads. It does seem sturdy enough to handle a decent amount of snow without issue. I don't think dry snow would be much of an issue but I could see wet snow being a problem.
I think if I found myself in a situation with a bed full of snow and a need to use the topper I'd probably sweep it out and then park it in the garage to let the last of it melt. Ideally if I had a trip coming up where I wanted to use it I'd go ahead and put it up ahead of time so I wouldn't get snow in the bed at all.
I think the biggest cold weather concern is being careful with that plastic so it doesn't crack.