I was famous once for skiing in the rain...back in the day:
I really wasn't skiing with an umbrella, the photographer asked if I would for the article. I had only recently learned to ski, and trying with an umbrella was...challenging.
Personally, I don't enjoy it - water always seems to have a way to enter in somewhere, and their are puddles on chairlift seats, etc. Wet snow falling is similar. Goggles also need constant wiping. But I do get the allure of having a mountain to yourself, soft snow, etc.