The Christmas and New Year holidays are the most annoying time of year because they cause the most havoc for almost every market's trading schedule. Some markets are closed completely, some markets are closed some days but are open other days, and some markets have modified opening and closing times on several days.
Knowing when your markets are open and closed is essential, otherwise you may find that you are stuck with an active trade, which you can't manage or exit until trading resumes after the holidays, during which anything could happen to affect your trade's profit and loss (that being said, professional traders will happily keep trades active during the holidays).
The holiday schedules for every market can be found at the appropriate exchange web sites. However, sometimes the holiday calendars are difficult to find, as they are often hidden several web pages deep. To save you the frustration of finding them yourself, the following are the direct links to several exchanges' holiday calendars:
US Markets
European Markets
Asian Markets
Note that some of the above holiday calendars include all of the necessary information (e.g. completely closed days, partially closed days, and modified trading times), but some of them only include the days that their markets are completely closed, with the days that their markets are partially closed shown separately (e.g. under the calendar). In other words, make sure that you check your markets' holiday schedules carefully, so that you know about all of the modifications to their trading times.