Here's a little info about helmets. DOT rating means that the manufacturer CLAIMS that the helmet meets federal guidelines. Snell ratings are given after a helmet has been TESTED and PROVEN to meet certain guidelines. Obviously, Snell is harder to get and is a better helmet.
As far a full face vs. 'street' style, I would NEVER wear an open-face helmet off roading. Some people will disagree with me, but the extra protection given by the chin-bar is invaluable in a 'quick-stop' type accident. Logs, stones and stumps are all out there on the trails waiting to slam your face into the bars. It doesn't cost any extra and, if you can tolerate the 'claustrophibic' feeling that is gives some people, wear it.
You don't want your nickname to be 'Toothless Charlie', do you?