I've ridden the GAP-C&O trails twice, all the way from Pittsburgh to DC. The first time, my bike had 700x32 Panaracer Paselas, which were fine much of the time but not wide or grippy enough for sections with mud or deep gravel. The second time, my bike had 700x33 Clement LAS (which measure 35-36 mm wide on my rims), and they were much much better. I had no problems riding on either trail with the Clements. In sum, I would recommend tires at least 35 mm wide with some tread. The tread doesn't need to be aggressive but slick tires are no fun in mud.