Have the same problem with the neck area . Solved it one day at a shoot .
Carry my rifle in a wool gun case , no frills kinda case . Real cold day at the range and I didn't have anything to wrap up in . So I thought "scarfs are wool , blanket is wool , what the heck ! Took the gun case and wrapped it around like a scarf and walla , instant scarf . As a side note , it works really well .
Steve