Cold hands are not a reason to stop bicycling in winter. You can fix cold hands with army surplus mittens that date from the Korean war. While there may be modern products that would work well for me, I have found that reasonable-looking bicycle gloves either do not keep me warm or are uncomfortable. I know other bicyclists who also consider these surplus mittens to be the best.
My army surplus mittens are shells that have supple leather where I connect with my bicycles. They are intended to be used with knit liners. The liner material is wool and nylon. The combination keeps me warm when it is too cold to use the shells alone.
Comfort comes from the generous size. All the samples I have ever seen are huge. It feels as if I am not wearing the mittens. Rather, I am inside the mittens as I am inside my house, not wearing them. Stylish padded bicycling gloves feel comfortable when I put them on, but soon after I start riding my hands hurt.
These mittens cause no interference when riding a bicycle. But beware, you will have difficulty fixing a flat wearing them. To be safe, when the temperature is in the single digits, ride with a friend who is also good at changing inner tubes. The two of you can share the needed bare hand time.
You can find these mittens on line by Googling “military surplus trigger finger mittens.” Prices are between $6 and $20.