Looks like it depends on what is being hunted but September marks the oveall start.. I'd wear something bright.
http://www.wildlife.state.nh.us/Hunting/hunting_dates_and_seasons.htm
Sept. 1 - Nov. 23, 2010 Black bear/end dates vary for method and WMU
Sept. 2010 - Jan. 2011 Waterfowl/dates vary by species and zone
Sept. 25-26, 2010 Youth waterfowl weekend (Saturday and Sunday)
Sept. 15 - Dec. 15 Deer/archery (Note: During September 15-30, archers may only take legally antlered bucks statewide; season closes on Dec. 8 in WMU A)
Sept. 15 - Dec. 15 Fall turkey/archery
Oct. 11 - Oct. 15, 2010 Fall turkey/shotgun (in certain WMUs only); Monday - Friday
Sept. 2010 - March 2011 Small game/dates vary by species and region
Oct. 1 - Dec. 31 Pheasant
Oct. 16 - Oct. 24, 2010 Moose (by permit only)
Oct. 23 - 24, 2010 Youth deer-hunting weekend
Oct. 30 - Nov. 9, 2010 Deer/muzzleloader
Nov. 10 - Dec. 5, 2010 Deer/regular firearms (closes November 28 in WMU A)