First off, congratulations! 20 years is something to be proud of. My DW and I have celebrated a number of anniversaries (without the kids), and some of the nicest ones have been in WDW.
You have already gotten the scoop on weather....I've always found it quite pleasant, occasionally sweatshirts in the evening.
I think you've picked the most wonderful time of the year to visit. The holiday offerings are unbelievable, and going in early Dec. you won't have any trouble with crowds.
Following is a link that lists all the special offerings for the holiday season:
http://www.allearsnet.com/tp/holiday.htm
Two things I would suggest you order prior to your trip. First tickets for MVMCP. I suggest going midweek as weekends can get more crowded, even early in the season. Don't think twice about not having children along...there is probably more for adults to enjoy. Second is a dinner package for the Candlelight processional. The actual show is free, but to be assured seating, I suggest one of the packages. There are links for the details on allearsnet.
You are staying at WL which is a truly festive and romantic site. One thing you can do from there is a "sleigh ride". Also their signature restaurant, Artist Point is a nice quiet place....I suggest the bison steak...:slurp:
Before I forget, with your hotel reservation (and if you've already made it, be sure to mention at checkin that this visit is for your anniversary. Also, whenever you make dining reservations, mention that as well. At the better restaurants, they often provide something special. We've been treated very well with some extra touches at Artist Point and Cinderella's Castle.
Other very good steak houses of note are Le Cellier in Canada (Epcot), even better is Yachtsmans Steakhouse at Yacht & Beach (and an easy walk from Epcot), Brown Derby in MGM, and Concourse Steak in the Contemporary.
Also from allearsnet (a very convenient reference), here is a link to the various restaurants and menu's:
http://www.allearsnet.com/din/dining.htm
While I recognize your self professed food preferences, consider an anniversary dinner at Victoria and Albert's in the Grand Floridian. It is the premier restaurant on the property, a grand way to spend a relaxing 2-2 1/2 hours on dinner, if you enjoy wine, they have great wine pairings, and some very special memento's. You MAY consider the offerings a little exotic for your palate, but they do offer something for everyone...and if you state your preference for beef, beef, beef, I'm sure they can prepare some special offerings not on the menu. Dining here is always the highlight of a celebratory visit.
Other things to consider include visiting the various hotels, particularly Grand Floridian, Yacht and Beach Club, Boardwalk and AKL.
If you want any additional or more specific info, feel free to PM me.