Yes it can be cold but it can also be hot! We've gone the last two first week in December's.
The first time it was freezing, especially at night and we needed our winter coats and the blanket I packed for my DD who was 14 months at the time. Really no swimming that year.
Then last year it was beautiful and we never needed our winter coats we brought. We also swam a lot and rented a boat etc...Georgeous!
Bring a variety of clothes and just keep checking the weather before you leave. That will really help you know how much winter or summer to pack.
Now, regarding the rest of info about going in December, the decorations are wonderful! Try to visit some of the resorts. Go to MGM at night and see the Osborne lights.
Get tickets for the
MVMCP; your grand daughter will love it! There'll be a special X-mass parade 2 times and hot choc and cookies and a pin and a free family photo and it won't be too crowded, although sometimes it can be but the rides really weren't that bad. There'll also be special X-mass shows. Tickets already on sale.
Then there's the CP at Epcot. That's a beautiful X-mass show with a choir and a narrator. Our daughters liked it. I was worried they wouldn't.
I love going that time of year because it's not too hot, crowds are down, and the Christmas stuff going on!
You'll have a great time!