This study, conducted in Japan, compared cooling of the neck and chest under controlled lab conditions. What is interesting is that effective cooling of just 2.2% of the body surface reduced sweating by between 16% and 22% with a significant drop in core temperature. Cooling the neck was a little more effective than cooling the chest, perhaps because the major arteries are close to the skin.
Wearing a wet multi-tube can be very effective in hot weather and effective neck insulation can make a big difference in the cold.
This infra-red video clearly shows significant heat loss from the neck: