My friend rode the Bike-Iditerod with temps over the several days at -20 F.
She wore pack boots with super gaiters. Wind shell mittens over other gloves.

They all still stopped riding about every 30 minutes and pushed their bikes to warm up their hands, face and feet.

i would try hand warmers inside mittens and over-boots.

And use cross country ski pants and jackets which are windproof on the front and stretch breathable on the back. Craft makes some nice ones.

Local cross country ski racers went to alaska to race. They said they wore 3 hats-
two on their head and one in their pants. The boys anyway.