I'd suggest the badge be called Snow Blower, but that's childish and incredibly immature so, yes, Snow Blower.
Love the invasion idea, btw. It'd probably need to be tempered down from every Winter Lord trial to being random? The WL trials seem to be run a lot at the beginning of the winter event and that could end up being a crazy amount of invasions all over the place concurrently. Dunno, but I really dig the idea of the invasion!