I love when drummers are open-handed and play a right-handed setup. It's so unusual but they make it work, and as a drummer I love feeling the groove that way. Drummer name / best song example in description
Traditionally speaking, drummers cross their right arm to hit the high hat and have their left crossed to hit the snare. Open-handed is self explaniatory from here. I think a lot of left-handed drummers play open-handed? Might be wrong coz I'm not a drummer.
Drummers will learn the most comfortable way for them to play. Oftentimes left handed drummers will learn how to a play a right-handed kit by not crossing their arms to play. Many drummers will even fuse the two styles in and out based on their own playing style; drummers like this include Tony Hajjar from At The Drive-in and Derek Grant, the current drummer for Alkaline Trio.