You can go any time you like, it's usually quiet. You need to pick up a free permit from the shop at the NC Botanical Gardens, just up the street.
Do not cross the ford when the stream gage height is 5 feet or above (currently 5.15). See https://tbg.carolinanature.com/masonfarm.html for some more info, including a link to check gage height.
No reservation needed. Just grab a pass from NC botanical gardens and make sure weather permits the crossing of the river to get there.
Tim is right. You will also want to consider the possibility of very wet conditions. To get to the reserve you will need to ford a stream with your vehicle.
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