Fawn Lake Country Club is an 18-hole private golf course in Spotsylvania, Virginia, built in 1997 and designed by Arnold Palmer. It sits in the $$ (moderate) price range for golf in Virginia. The course is open all year. Tee times can be booked 7 days in advance. Play is generally limited to members and their guests.
Details like fees and seasons change, so call the course before you head out.