Becky - what a great idea! I've wanted to eat at the Blue Lagoon but the menu looked pricey and not to interesting for my daughter. Having just dessert is a great idea! Will they frown on this or is it acceptable?
As for traveling with a 4 year old in the winter - we were there last January, and while granted, my daughter was 12, we still both love the fantasyland rides, and we really appreciated that there were NO LINES! Your and your little one will have a fantastic time despite the cold! Not having to stand in line for Peter Pan, Dumbo, and etc. will more than make up for it. And as others have already mentioned, there's always hot chocolate and plenty of indoor attractions. We bought our APs when we were there in January and they came with a bunch of Fast Passes that could be used any time (unlike the usual fast pass which has a certain time slot and day). We did not use a single one! There simply was no need, because, (am I repeating myself) there were NO LINES for anything. So bundle up that 4 year old and have a blast. If you have specific questions, keep them coming!
Jody