If you have a lathe - that would be good. If not, try to find somebody who does and would like to help you. That being said, any good sharp tool will cut any hard wood. A spoke shave is an old time tool that can transform square stock into round stock. You could even take a common bench chisel, cut into the corners and quickly make a rough octagonal rod. More gently cuts can transform that shape into a more rounded piece. Patience will get you close enough and lots of patience will get you close enough to finish the round. As for the groove - carving tools with lots of patience. First, draw a thin spiral line and cut along it. Using lots of patience, cut that groove deeper and wider. To help you draw that groove, use masking tape to protect the uncut wood and draw your line on an edge.
Its' never hot or cold in New Hampshire... its' always seasonal.