I have gone to Disney World in December three times. The first two times, I went the first week in December, and the third time was this past December 11th through 18th.
The weather will be a lot cooler than in the summer months that you are used to. Low to mid 70s is probably a good estimate of what you can expect temperature wise during the days. Each time I've gone in December, we always wore jeans and sweatshirts in the evenings (or sometimes simply put a sweatshirt on with shorts in the evening). A light jacket is also a good idea. This past December, I wore jeans and a t-shirt to the parks all day on 6 of 8 days because it was so cool while we were there.
December is a great time to go because there is so much extra activity going on. You should definitely catch the Candlelight Processional at Epcot. It's an incredibly moving show. Watch for the dinner packages to go onsale during the summer. They run in the $40 range, and include a full meal (appetizer, entree, and dessert--no drinks), and reserved seating for the show. You'll also get 15% off at your purchase at Epcot that day--we saved at least the cost of the dinner package by saving most of our shopping for that day.
You should also plan on going to Mickey's Very Merry Christmas Party at the Magic Kingdom, which costs about $35. They have the Christmas parade, special fireworks, and holiday shows. It also includes a family photo, and cookies and cocoa. And it snows on Main Street. It's a lot of fun, and well worth it. Tickets usually go onsale in July or August.
It's also worth going to the resorts to check out the holiday decorations. I went to several resorts, and loved the decorations, especially the huge gingerbread house at the Floridian and the carousel at the Beach Club.
The shorter park hours aren't too big of an issue. The parks aren't as crowded so you can get more done in less time. It also gives you the chance to experience things outside of the four main parks that you might not see in the busier months. We spent a lot of time at Downtown Disney on this trip, which we didn't always have time for in the past.
You should check out the trip reports section. A lot of people have posted their trip reports for December (including me).
Hope this helps, and have a great trip.
Karen