1:21 p.m. on February 12, 2007 (EST)
There have been several good suggestions already. Lessee if I can summarize and add a couple comments.
For the range of temperatures you mention, the layering concept is the most workable, and is what I use in everything from summer Sierra (and many years ago in the Smokies) to Antarctica last month.
1st layer - thin wicking liner of poly
outer layer - windproof shell glove or mitt, depending on conditions, and if in rain or snow conditions, waterproof as well, Goretex or one of the Gtx clones.
midlayer - fleece of mid to heavy weight, depending on conditions (if you are actively hiking or working, this is optional, since the liner may be enough warmth even down to the 15F you mention.
With your poles and some other conditions, you might want to consider the outer shell having a leather or grippy synthetic palm. The thin liners don't stand up well to heavy usage. Full leather gloves also have their place, but may be overkill for what you describe as your usage.
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Basically, on your skin, you use a light liner glove. For most purposes, this should be a wicking synthetic (poly of some sort, which OR, Manzella, Patagonia, and others make - and are even available at WalMart, Target, and others). I wear these in everything from dayhikes in cool conditions to the Arctic and Antarctic. If I need to manipulate something that requires too fine a touch for the full set of hand covering, I can pull my hand out with just the liners still on and adjust the camera, re-tie a boot lace, manipulate a zipper, whatever, without losing too much heat or sticking to the metal that is at subzero temperatures.
The shell is the next thing - this provides the wind and water protection, and the gripping surface. If it is really cold, gloves with separate fingers are much colder than mittens. I find I can often use just a mitten shell (I use the OR expedition mitts) with the light liner glove and keep my hands warm in conditions where a fully insulated glove leaves my hands feeling cool.
If it is too cool for a shell plus light liner, I add a medium to heavy fleece liner in between. This reduces dexterity, but increases the warmth. For really cold conditions (Antarctica last month on summit day), I go to mitts with a heavy liner (the OR expedition mitts). I still have the light liner gloves on for those times when I want to use the camera or manipulate a zipper without exposing my hands to the full-on -40F with a breeze.
Several companies sell "system" gloves and mittens with removable liners. Or you can "build your own". Be sure to try the combined layers together in any case, since you need room for the inner layers to allow circulation and dexterity. Thus, I use large or extra-large outer shells.
There are lots of good companies out there. You can get good enough quality cheaply for the thin liner (they wear out quickly anyway, and you will probably want to have a couple extra dry pairs in your pack, even on a day hike, if it is raining or snowing). But the outer shell should be from one of the better quality companies - Outdoor Research (OR), Black Diamond, Cloudveil, etc.
Oh, I should mention that for some purposes, I do use a fully insulated glove, like Cloudveil's ice climbing glove, or Black Diamond's Guide glove - these use Schoeller for breathability and some water resistance, plus padding for banging one's knuckles on the ice. I still use a thin liner, though.