Yes, many things are closed during the Christmas holidays in Prague and Cesky Krumlov, but many places are open too. Its not hard finding something to do or a nice place to eat. I've spent two Christmases in CK and I love it there. Everything is pretty much business as usual, except inside the castle is closed. You're free to roam the grounds, including the gardens though. While not in bloom, theyre still worth the walk to the top of the castle.
I wouldn't suggest being in Vienna during this time. In addition to Christmas eve/day, they also celebrate Advent, so a lot of places are closed the 26th too. Prague starts getting back to normal even Christmas eve night, with plenty of places open Christmas day. This year I will arrive in Prague on Christmas eve, and spend the holidays there. Am also considering a side trip to CK again this year too. The Student Agency bus goes to and from Prague and CK all day on Christmas too
The trains run all the time. no days off for holidays.