Hi Star!
The Disney Parks do not close for the Christmas holidays (or any other holiday!). In fact, some of the longest park hours are found on these holidays!
Value Seasons do vary slightly by resort category. The best way to check the dates of each season is to visit the accommodations page for a resort you are interested in and locate the "Room Types & Pricing" link on the left hand bar.
For example, if you are interested in the Port Orleans - French Quarter resort, you would visit this
page. Once there, locate the Room Types & Pricing
page. The default will be to show you the dates for the Value Season - Weekday rates, along with the corresponding dates. On this page, you will also be able to change the dates/seasons by using the "Season" selector on the right of the page.
In general, a good rule of thumb is that the value seasons follow the school schedule. When school is in session, prices will be lower. During vacations and holidays, prices will be higher.
Hope this helps! Don't hesitate to ask followup questions if you'd like more information on any of this!