As Roger says, arms underneath. Or if you use trekking poles, keep them out-your arms will be working hard and have plenty of bloody flow to keep them warm. Add waterproof mitts if you need to (eg Zpacks or MLD, or MYOG). Not too much need for longer arm coverage. If its really cold for me personally, I would wear my windshirt underneath but it would literally have to be sub freezing temperatures (personal). If its sub freezing, my windshirt sheds frozen stuff no worries.
Another option, which I've been toying with, are arm warmers aka cycling. Most cycling ones stay away from, they are spandex. But I've been thinking for a long time that I'd love to make a pair of ones that just do my upper forearm, out of polypro (when my daughter wears out/outgrows her toddler polypro pants, I'll cut the legs off for this purpose). The wrist area is where a lot of heat comes out. In the snow in Japan I was finding if I just cover this area (they sell such things out of cheap fleece material in Japan for a buck) my hands and forearms stay warm. The polypro could get wet and still function, that much thin polypro is easy to squeeze out and dry, they are easy to take off and put on wet (unlike wet polypro liner gloves).
I would definitely try the waterproof mitts first and see how you go, before you make something more complicated like you describe. Silnylon would be fine to try to start with, there are plenty of mitt patterns and MYOG threads out there.