I hate to say it, but Eric's is the voice of reason in this one.
You can spend the next couple of years, and a whole bunch of cash chasing the dream of dry hands, or change the way you think about it and start enjoying the conditions now.
When people talk about having dry hands, they almost always mean they want warm hands. Especially if they're just out for the day, or if they're able to dry their hands out properly at night. If we go with this as a basic premise, all the rest changes.
The two simplest ways to do this are fleece with a wind barrier over the top, or wind/vapour barrier with an insulating layer over the top.
Option one is great. Go with a Powerstretch type layer. (I like my BD Midweights) Over the top of this goes an extra heavy duty gardening rubber glove. Conveniently these come in black. It can rain on these babies all day. You can dig in the wet snow. You will have reasonable dexterity. It will cost you about $25 (Because who would buy at full retail). For the total system though, a second pair of liners makes it perfect. These get kept in an inside pocket, and they get swapped out when the ones you are wearing start to get too wet. Because they will get wet, either from your sweat, or from water leaking in through the big hole at the top! Put the dry liners on, put the rubber gloves back on, squeeze out the wet liners, and put them in the inner pocket to dry/warm up. The only problem with this system is that it probably isn't durable enough for scrambling or heavy rope work.
Option two is also pretty good. Pick up some nitrile liners. These are like surgical gloves, but much tougher and not as stretchy. They should be available in your supermarket for about $10-$15 for 100 gloves. These go on first. Over the top of these, go with whichever pair of the Mechanix type gloves match the temps you will be out in. Avoid anything with natural leather, as it is slow to dry, and less durable when wet. Their Winter Armour, Safety Fastfit or Material 4X Original all look pretty good. This combination will be a bit less warm, although the barrier/liner glove makes it pretty good, but a bit more dextrous and much more durable for scrambling. Not great for digging around in the snow though.
Of course much of this was derived from Andy Kirkpatricks rant on gloves
and a couple of years and several hundred dollars worth of gloves used in Victoria, Australia, which is a bit like the PNW except wetter and with much crapppier snow. I now use option one when I'm wet in the snow, and option two when I'm wet in the bush. If I'm going to be mixing it up, I take both systems, without the second set of liners.
This works for me from -15C to about 10C. Any warmer than this, and I generally don't use gloves.