I live about an hour from Branson and have been there MANY times. It will be cold - probably in the 40's during the day, but that can really range from
30s to 50s. The nights will get cooler/ colder - and remember it is in a mountainous area.
As far as what to do - there is outlet shopping, there will be alot of music shows having Christmas programs. There is a nice shopping/ dining area called the Branson Landing that is on the water. There is also a "Riverboat Cruise" - I think called the Branson Belle that will probably have a Christmas show.
It's a very family friendly town, so you won't find alot of bars, etc. Think Vegas, but without any sin!
If you want to know anything more specific, please feel free to PM me. Also, if you want to tell me where you are staying, I can probably let you know what all is nearby. Since I live an hour from everywhere, Branson is one of my places I go on a regluar basis to do shopping.
ETA : I just saw that you live in Washington. I feel kind of silly telling you that Branson will be cold! ha, you may think it's sweltering there from where you are coming from!
SAHM to Pete and Repeat my "Irish Twins" - DD 12/06 and DS 11/07
Never argue with an idiot. He'll bring you down to his level, then beat you with experience.