have you tried any Mechanix gloves? they do have an insulated pair but don't know how they would be feeling a trigger. I use the regular classic style in when outside in winter.

Seirus gloves (the midweight ones) work for me.

That sounds like a shitty condition OP, sorry to hear it.  I'm tagging this because I shoot a lot in the cold and everything that keeps my hands warm a little bit
seems to limit my finger dexterity when I'm working with my pistol.  The rifle is more forgiving, but not so much with the pistol.

Might be able to go with a thinner glove if you use the heaters in the backs of them.  Some gloves have pocket for them.

Do you just need something to cover your hands or need decent insulation too?

I tend to wear gloves during a significant portion of the year....

I find I can manipulate everything I need with a rifle wearing a well loved pair of Black Diamond Patrol gloves. They're almost 100% leather, so the key is buying a touch on the small side. Once they pack out a bit, they fit perfect for medium dexterity activities. I can shoot, reload, rack, and manipulate my pistols with them too, I just can't fill pistol mags. I keep my AR food on stripper clips, so loading those mags is easy with the gloves.

They may be more than you're looking to spend though.

Take a look at under armour cold gear liner gloves.  I don't use them to shoot but I do use them to drive on sub zero days when the steering wheel is freezing ass cold.  I also have a pair of heavier gloves that came with a similar liner and the outer glove even has a zip pouch for hand warmers.  I tend to keep this set in the vehicle for emergencies but I used the liners a lot this last winter.  I tend to keep a half dozen pairs of ragwool gloves with grips dots and no finger tips for all outdoor activity but these synthetic liners have won me over for general use.

I have a pair of nomex gloves with soft leather on the palm and fingers that I use for chainsaw work and have shot with a lot.  They cover the forearms and came from Blackhawk over 10 years ago.  Great shooting glove, sucks in cold the moment they get wet.

The heavier glove with liner I think came from lands end, I will check.  You don't want to shoot with them, but having a heavier glove to slip your hands in and out of with the liner glove still on is a classic winter trick.  You hang the gloves or mittens on cord long enough to allow full arm movement but they hang on you when you are not using them.  You wear liners to do work with and then slip them back in to the mitts to warm or for more protection.  It's overkill for 40 degrees but not for you.  I have a friend here who has developed something similar, I am thinking it is actually the same condition.  She gets it on her arms and hands and has to bundle up just to step outside.  They say she is alergic to cold but this makes complete sense.  She can't even go in the walk in freezer at the restaraunt they own without sleeves on.

Perfect time to buy high quality gloves on the cheap.  Keep an eye out here.  Should be able to find some very high quality gear for quite cheap.

I think mine are the "original all weather gloves."

I picked up a pair of shooting gloves at Walmart.  They are leather and thinsulate.  I have shot trap in the winter when it was 10 degrees out with out any discomfort wearing these gloves.

These are great, I was given the same pair but from our Snap-on dealer and found them good almost down to 0F for more active pursuits like snowshoeing. I ended up giving them to my carpenter brother and he loves them. They have similar dexterity to Nomex flyer's gloves.

The insulated mechanix are way warmer then the regular ones I have used.  My insulated kept my hand warm in to the 20s.