Can you please tell me when museums and attractions might be closed from December 21st to January 10th?
There are many attractions in Tallinn, and they have their own arrangements. It would simplest to decide which you're interested and check their websites for up-to-date info. Apart from the 24th and 25th December and 1 January, there won't be many wintertime attractions closed. The Christmas market last year continued till the Orthodox Christmas, 6 January.
Some attractions (mainly museums) are closed on a Monday. This link will hopefully help:-
A few attractions are also closed on a Sunday or Tuesday so it's always best to check the opening hours before hand.