The weather is extremely changeable so I am of the consensus that you should take it and then you'll have it. If you don't need it, no biggie, but if you do then you aren't running around spending mucho bucks on a WDW coat (unless you really want one!).
We are from Western NY, grew up in Buffalo (can you say blizzard?) and we still bring our winter coats and will do so when we leave in 18 days.
During our Jan trip (2004) it was chilly and cold for most of the trip, the morning I ran the 1/2 marathon the temp was in the low 30's and I was freezing. Hats & gloves are a must to keep warm, they don't need to be fleece lined hunting caps, just a knit hat was enough to keep warm. I also brought the cheap
WalMart gloves (not the magic gloves, but the other thin ones they sell) and those were enough to keep up warm & toasty.
Jan 2006 was a bit warmer during the day but still cold at night. DH & DS wore hats at night (they have short hair) and were used our heavier coats most every night except for maybe one. Still wore sweatshirts over our LS tees that night too. DH wore shorts 1 day and really froze so we might pack 1 pair each of those if we get a warm day or 2.
For the poster who asked about the jackets, we do lightweight jackets or sweatshirts in the AM (like thin polarfleece) and do take them off when it gets warmer. I usually fold them up quickly, roll them as tight as I can & put them in the bottom of our backpack & we do fine that way. With 5 in your family you might think about the locker or tying them around your waist.