Move them inside? Inside something like an arena, perhaps? Sounds good to me.
It's been a while since I've been to one during the winter, or even in San Myshuno at all, but I seem to remember a festival having heating towers. Might be just mixed memories.
Either case, making sure your sim has their winter clothing on should help. If you do want to enjoy the festivals more, making sure the severe weather isn't on would help. It would be a downer to be only just getting to know the living statue and they got struck by lightning. (Interacting with the living statue enough and you get their wardrobe added to your sim's inventory)