Perhaps a distinction needs to be drawn between a "calendar-winter ascent" and a "wintry non-calendar-winter ascent". But that distinction is clumsy enough that it would probably never be used. So maybe instead we should just talk in terms of "wintry" ascents. But that would not seem to do justice to wintry ascents done in calendar-winter.
Since the four-season classification system is causing so much trouble, and since it is contrived anyway, perhaps we should take steps to do away with it altogether.