We go often in winter months. I don't really notice more closures, but some rides open later than others. All the parades run every day (except Spectro, but they post it on the website, you can plan accordingly.) I can't think of any show that isn't running, except that the Poly Luau doesn't go if it is too cold...if it is a concern, book the earlier show (temps keep going down in the evenings!)
The difference between summer and winter is night and day. No crowds, pretty much walk on to everything except the biggie rides. The stores are browse-able. You can walk around the park easily, without having to weave through people, or getting banged into by anyone.
When there aren't so many people around, it is easier to notice the beautiful landscaping or little details that you would just miss when surrounded by bodies.
The parks close earlier, but you can stay in the park longer in the morning because it isn't so hot and crowded. Shorter mid-day breaks are fine when you aren't worn out from racing around trying to beat the crowd and being in the heat.
Waits are shorter everywhere - for the security lines, to get in to a park, for the monorail, at a restaurant, to pay for merchandise. Even less traffic.
And you do not have to deal with that oppressive and unrelenting heat/humidity. That alone is reason enough to go at a down time.
To me, it seems everything is easier and more pleasant in the winter months.
eta: Oh, and congratulations on your up-coming nuptials!
