As most of you know, I live in the great white north. -37C is no stranger to me.
For chores, I wear thin gloves (my recent faves are ceramic-infused back on track gloves) inside of mittens. You want mittens to do chores, preferably fleece-lined wool mittens. You also want the ability to take them off. Sometimes I wear wool mittens with flaps but they tend to annoy me so wool mittens over gloves do the trick, and I can take the mitts off briefly if I need to. The fleece lining inside prevents my hands from getting wet if I'm handling a lot of snow.
But for riding, you want to take it to another level. I often buy gloves at Mark's Work Wearhouse, but I believe that's a Canadian company. I generally buy men's smalls because annoyingly, women's gloves are never heavy enough. They're warm, but they will wear out if you use them for anything other than riding. Then there are the mittens with the split fingers so your three first fingers are together, but your pinky is separate for holding reins. I wear thin gloves under those too because they're never warm enough. They're ok, but not my first choice. I do prefer the really thick gloves, and sometimes will wear my BOT gloves underneath for extra warmth.
In the end, it is possible to keep your hands warm. I tend to have poor circulation to my extremities, and ride in bitterly cold weather all winter long outside, but my fingers are usually ok if I wear layers. Toes, not so much.