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I dont know anything about helmets, but it might not be the amount of padding that matters, but maybe the material.
Like maybe a skateboard helmet's padding will get a lot harder in cold weather and not absorb shock as well...
^That may be a possibility, but I think overall a skate helmet is meant for harder impacts, as pavement is usually less forgiving than snow, depending on the conditions of course. To make up for the possible "hardness" of the padding due to the cold, you could wear a hat (meaning beanie) underneath. I have a skate helmet that I wear for railjams with a beanie underneath, and it works fine. RED also makes a bunch of skate/snow helmets that are hybrids between the two, meant for use in both environments. I think you should be fine.