The best time to go to Fredericksburg is October. The weather is sunny, relatively warm, with temperatures in the low 70s and generally dry, with limited rain falls.
While visiting the wine country we recommend you attend the very fun Oktoberfest in Fredericksburg, from October 4 through October 8. Prices for accommodations surge during this week, so if you're on a budget try to avoid early October.
Valentine's Day, in March, is also a nice time to visit. Fredericksburg is a popular romantic getaway destinatin with nice Wineries and great restaurants.