I once went to Prague one week before Easter (c.ca 1994) and I have never felt so cold before or since, so imagine that in jan. it would be even colder!
Just back from Prague and it was very, very cold. We landed to 4" of snow but it quickly cleared leaving us with cold bright weather. Remember that the streets of Prague are cobbled and you may need to consider walking boots. I just took sturdy flat shoes and wished I'd taken my boots. Scarf, gloves and hat are ESSENTIAL! Had a great time though.