An easy approach - wear "chopper mitts" over your regular gloves. When it warms, pull 'em off and stuff in your handlebar bag or pocket. Chopper mitts - large deerskin mittens warn to chop wood. Used with wool inner mittens when cold and alone for both warmth and grip/blister protection in warmer weather. Not traditional riding wear but they work really well. (Get the largest size you can get. I have long fingers, skinny hands and wear the XXLs.)

I don't ride brifters so I cannot say how well the work with the shifting. For DT shifters, they work just fine.

Chopper mitts - my preferred winter wear for the past 50 years. (Treat them once a year with Snowseal, more often if they get wet a lot.) Google chopper mitts and get the deerskin ones. You will see a bunch of choices. Skip the lined ones. Good pairs have moccasin style stitching. Best have a loose web between the thumb and forefinger but I am not sure that makes a difference. Prices are al over the place from around $30 to $70+.

Thre are plenty of cloth over-mitts but I stay clear of them because they are slippery on the handlebars. Properly treated choppers are wonderful for their grip. (First ride after treatment, sticky, but after that, close to perfect.)