Hi, Marnie!
If your family can travel to Walt Disney World during a non-peak season, while the weather is mild, I suggest checking out mid-to-late October through mid-December (excluding Thanksgiving week.) This is considered a more economical time to travel if you're also looking for mild weather and lighter crowds. According to the unofficial site, touringplans.com, crowd levels tend to be fairly low at this time, with the exception being weekends and, of course, Thanksgiving week. If you head to WDW during October and early November, you'll have the added bonus of seeing the parks all dressed in their fall finery, in addition to, perhaps, the
Epcot International Food & Wine Festival. You might want to book a visit to
Mickey's Not-So-Scary Halloween Party, too, which is a separate ticketed event at Magic Kingdom that's sure to get the entire family in the mood for trick-or-treating. Keep an eye on WDW's website so you'll know when those dates will be announced for 2013.
Other seasons bring milder weather with crowd levels that are lower, too. If you can travel after New Year's, but before Valentine's Day, the parks are generally less crowded. You might be in Orlando during its average January high (according to weather.com) of 71 and average low of 47 (really wonderful for touring the parks); however, we've been in Orlando in early January when a cold front brought the daytime high to 36. Weather fronts can be unpredictable, but this might give you an idea of the normally milder temps in conjunction with lighter crowds.
Send some dates and we can look to see what special events might be going on at those times, too. I'd love to help you find that perfect balance of timing, events, lighter crowds and milder temps. :-)