Timberlake is just north of Durham, and I believe it has very similar weather. Expect no snow, or maybe once or twice per winter a light dusting. Rainfall in this area is fairly constant throughout the year, 3-5 inches every month. We still have plenty of sunny days throughout the winter. Yesterday was gorgeous and clear, the next three days are supposed to be sunny, then the next four after that partly cloudy, before the next storm. We're in a drought right now, but there were still plenty of clear, beautiful winter days last year!
If you're looking for peace and solitude, but still want to be close to Durham and the Triangle, I'd suggest also looking in Chatham County. The closer you get to Jordan Lake, the more expensive, but there are homes in the $250s-350s at Cattail Creek (heavily wooded, 1.5+ acres), homes in the $400s+ at Cedar Grove (2-7 acres), and also land and single homes for sale scattered throughout the countryside. There are a few other developments as well, but it sounds like you're looking for some land of your own.
Chatham County mainly consists of gently rolling, heavily wooded land, interspersed with a few farms. There are recreational areas at Jordan Lake and the Haw River, but mostly very quiet and peaceful, though most areas north of Pittsboro are within 15-20 minutes of shopping, etc in Apex or Chapel Hill.
Hope this helps!