I did about 20 miles east of Harper's Ferry last summer with 700Cx32 with little trouble. I was fortunate in that it hadn't rained too much the previous week, so there were only a few puddles, and only one that was long, deep, and muddy enough that I slipped a bit. It was a little rough, but no problems rolling. The surface did ride like a poorly maintained road.

It's a tough call, frankly. If I were planning a multi-day trip, I'd go with 35 or 38s (if the bike could handle them) for a bit more smoothing. Fatter tires on a mountain bike would be counter-productive if you're planning to ride significant daily distances, unless they had very little tread.