Is it a bad idea to put in replacement windows in the winter?
I see no particular reason that installing windows in December is a bad idea--assuming it can be done quickly enough to not freeze to death or have rain/snow ruin anything. You may want to make temporary living arrangements for a few days while the windows are being installed. 

My recommendation is to go somewhere other than a big box store. You may be able to get them MUCH quicker else where. HD told me it'd take 12 wks to get in Andersen windows-- I got them thru a local HW store in 4 weeks--for less money.