I took a Scout patrol east to Antietam last year, and we all rode mountain bikes. We had one night of heavy rain, and found the trail extremely muddy the next day. Trail-wide puddles, miles of mud. The mountain bikes were a good choice. The two who left their fenders home were a muddy mess from head to toe.

You could probably ride in on 23s, but I'd recommend mountain bike tires with fenders. That's what I'll be using this year when we return for Antietam to DC and back. I'll be busy enough dealing with Scouts, I don't need to worry about navigating around mud puddles.