I have occasional bouts of Reynaud's as well. The OP's right about it not being worth going to the doctor. Medication should be a last line of treatment for any physiological issue, after less invasive and non-chemical means have been exhausted. No matter what you want to believe ALL medicine has side effects. A persons hands get cold, so you put them on blood thinners? That's extreme, and it will definitely have side effects, even beyond alcohol-related ones. For example, suppose you're on blood thinners, cycling in the winter cold, and you're in a crash and start bleeding profusely. Not necessarily a good situation, esp. when you're worried about potential hypothermia. I'm pretty sure that will effectively shorten your survival time...all for warmer hands? No thanks. I've been going with Polypro liners under windproof gloves, and they help a lot. You might look to get one of those squeeze balls to exercise your hands in down time. Increasing your muscle strength there should help a good deal with circulation (unless you happen to have some arthritis, as well.)
Good luck, I sympathize.