Even though it’s the middle of the night, there’s snow on the ground, and they’re in pyjamas, Lorelai and Rory put on coats and scarves and walk to Sookie’s house. In other episodes, they say that Sookie’s house is a long walk from theirs (they seem to have to go through the centre of town to get there), but for some reason they always walk, even when complaining about the distance. Apparently it is both too far to walk quickly, and too close to drive (perhaps a mile???).
In real life, the sets for Lorelai’s and Sookie’s houses were right next to each other, and could be accessed through a door between them. Note that there are still snowmen standing from the previous episode’s contest – apparently they are left up until they melt in early spring.