Many people mistake common water snakes and hognose snakes for venomous ones. Rangers have told me they have only seen copperheads in rocky areas and that other types are generally unheard of this far north. You'll see black rat snakes and a few others, but they'll usually take off pretty quickly.
Depends on how warm it is but in early February they most likely won't be seen. Just keep an eye out and stay on the paths. Eno river is home to many snakes including copperhead, cottonmouths, and rattlers. As long as you pay attention you should be fine though.
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