As someone who spends 12 months a year traveling the world coaching mountain biking, mountain biking and racing I have my favorite spots! I will start with the continental United States and deep winter (Mid-December through Feb.). When 90% of the country is freezing there are a few spots I love to ride in.
We will start with South Mountain. At over 16,000 acres (for comparison Vail Resort is the largest single mountain ski resort in the US a 5,289 acres) and over a thousand vertical feet it has great trails for advanced beginners to pros. South Mountain is my favorite place to ride in Phoenix as it has some of the rockiest, most challenging trails in the country that always keep me on my toes.
North of Phoenix off of I-17 is the Black Canyon Trail which has several trail heads and will one day go from Flagstaff to Tucson. It has quite a few fun sections all not for from I-17.
For late fall and late winter riding (Mid-November through December and mid-February through April) all of the above are great with Sedona and Boulder City warming up quite a bit.
Other favorite late fall and late winter destinations are Austin, TX, Albuquerque, NM, Saint George/Hurricane, UT and most of California.
I have purposely left out a lot of great trails and areas near those above has we live in a big, beautiful country, go out and explore!