The surface under the mud puddles is hard and provides good traction. I always ride through the middle of a puddle if there is mud everywhere else. But slowly, as you will make a worse mess of your bike and clothes if you go fast. One C&O trip I had to stop frequently to remove the build up of mud between the tires and fenders, but most of the time the water in the puddles keeps that area clean enough to ride.
The resurfaced areas are very well compacted, so I find them good to ride when wet.