I'm in the mountains a bit west of Grunt. We have humid summers and dryer winters. My favorite bow wood is osage but hickory ain't too far behind if kept dry. Any of the whitewoods should be cut during the growing season so the bark will peel off and you don't have to chase a ring; just use the wood under the bark for the back. Like Grunt said, don't let any whitewood lay on the ground for any length of time. Cut it down, split it and get it in a dry location to begin drying. It will begin to rot if left on the ground for a week in warm weather and you won't know it until it breaks while tillering.
Osage, locust and mulberry can be cut anytime you can get it. You have to(eventually) get the bark and sapwood off and build your bow with the heart wood(not completely necessary but the norm). If you leave the bark on osage to cure treat the bark with an insecticide to kill the grubs that have been laid in the bark or they will eat it up. When you remove the bark and sapwood from either of the three mentioned above seal the ends and back very well. If you leave the bark on to cure seal the ends.
Either of the oaks make good bows. I'm not sure about the silver maple but I think green ash isn't too good.