Get a cheap winter cap from the dollar store, cut the top with scissors, invert it so the cut portion is invisible inside jacket, when you pull it down over the neck. It is actually much better than a regular neck warmer as it hugs the neck due to stretchable material and prevents cold air from going in the jacket
Good idea. I’m lucky in that my wife is always altering her clothes. Ended up with a fleece neck gaiter that’s the perfect length when folded in half.