I mean they did seem to emphasize the need for warm clothing in the cold environments, like when Kirito went with Liz that time. But I can't think of any actual effects it would have... Maybe a status effect? Similar to paralysis but with freezing?
It should be noted that Lisbeth and Kirito did wear cloaks/jackets when going to see the dragon, so I suspect you would probably feel rather uncomfy at least :P
