Double mittens. Leather outers, wool or synthetlc wool-like inners. Pull the inner out when you get to work. Easy. And while riding and it warms up, pull the inners out and ride just the leather outer.
Look for deerskin "chopper mitts". Keep the leather treated with Snowseal. (Twice a year works for me.) Buy the mitts in the biggest size you can find. I have thin but long hands. Large is too small. XL OK. XXL my fav but hard to find.
I've been riding that combo since the '70s. It simply works. (Although some modern shifters might be a challenge. I put away my derailleur bikes for the salt and snow months and ride fixed so I'm in bliss.)