Fall, with winter coming in second for favorites here in Wyoming. Spring is too wet and depressing, but luckily doesn't last long, and summer gets WAAAAY too hot here...I can handle -20 in the winter here much better than the 100+ during the summer, it's a lot easier to warm up than cool off. We never get to travel, but if we get into the position to be able to do so we will probably aim to travel in the spring or early summer.
I love winter the most and we usually do most of our traveling in December. My husband and I both have birthdays in December and we were married on Christmas day, so that is out favorite month to travel and celebrate.