A completely round cross section is a bad choice for hickory. There's not many woods that can handle a round cross section. Why do you want to make a round cross section in the first place? It's difficult (but not impossible) to turn a board to a round bow. Far easier - esp. for a beginner - to make a square-ish cross section out of an already square board.
To add to that, a board of only 2"x 2" is likely cut at an angle from the tree. Even the slightest angle will mean you cannot follow the grain continuously and still end up with enough wood to make a bow. A 3"x 3" would give you a lot more leeway.
Read the first chapter of TBB1 to get more info about wood properties.
Post some pics of the board so we can see the growth rings running along the entire length.
