We do need a permit which isn't hard to get as long as you have enough land to raise them on.
New Hampshire has a few Red Deer and Elk farms that I know of but I haven't seen any for whitetail deer which doesn't surprise me as some states just won't allow it. As for the states that do allow it I think there are over 35 states that allow whitetail farms and all of Canada. Here is a list of the Red Deer and Elk farms in New Hampshire that I know of.
Bonnie Brae Farms
Plymouth, New Hampshire United States
Corn Hill Farm
Boscawen, New Hampshire United States
K.M. Ranch Inc.
Nashua, New Hampshire United States
Kear-Wood Farms, LLC
Wilmot, New Hampshire United States
Sunset Ridge Ranch, Inc.
Nashua, New Hampshire United States
Twin Oaks Deer Ranch
Boscawen, New Hampshire United States