I always thought of the Winter being Faith's mind/soul. Much like it is in the Otherland books. So when Faith goes away, so does the Winter. The doll house would then be a part of her mind in which she has locked herself from all else (except apparantly Faith and the White Lady). If the Winter (Faith's mind) would in turn be somehow in the Storytime, it could be messing up things there.
If Waticorp used Faith to create the Dreamer device (so that people would be able to control their dreams), their control of Faith/the Winter - and thus indirectly Storytime - would be a very good way to manipulate things.