Having grown up in Anne Arundel County, and having spent a lot of time swimming in the Severn and wandering in the woods throughout the area, I've heard a lot of speculation about snakes. Cottonmouths, Water Moccasins, and Copperheads, oh my!
The truth is cottonmouths and "water moccasins" are the same animal (Agkistrodon piscivorus) (see below). The northenmost range of this critter is the Dismal Swamp, which spans from the southern border of Virginia into northern North Carolina. They aren't found in Anne Arundel County, in fact, they aren't even found in Maryland.
Northern copperheads (Agkistrodon contortrix mokasen) are found in Maryland, and are one of only two venomous snakes found in the state. The other is the timber rattlesnake (Crotalus horridus horridus), which is found only in the western part of the state now (though historically found at least as far east as Calvert County).
That having been said, in all my time out and about, I've never come across a copperhead (below), and verified reports of encounters locally are very rare. Though one longtime resident of the Crownsville area did tell me that there's a copperhead den in the Bacon Ridge Branch area, and that you know if they're about because "the smell of cucumbers will be in the air." If you've seen one and have pictures, I'd be very interested to hear about it.
Chances are, if you see a snake in the water, or around the water, it's a northern water snake (Nerodia sipedon) (below). This snake is non-venomous and feeds on fish, amphibians, and small mammals, like mice and muskrats.
In any case, if you do happen across a snake in your yard or on the river, just keep your distance, make some noise, and it will almost certainly be on its way. These reptiles, even the venomous ones, are an important part of the river's ecosystem, and help to keep many other nuisance animals in check.
Additionally, it is illegal to kill or possess native snakes in Maryland without first acquiring a permit from DNR.