I've never found a glove I would consider shooting in, no matter how thin, so my "cold weather" strategy is to eliminate as many places for heat loss as possible. I don't want to be "just over cold", I want to be "warm".
I start with a UA skiiing base layer. Very warm, yet still very flexible; this impacts my movement VERY little if at all. I only add the pants part of it if it is truly sub freezing howeer.
Other stuff: Knit cap. Heavy overcoat any time I'm not shooting. Hand warmers in the pockets of the coat. Wool socks. Basically anything I can to keep the rest of my body warm, I find will help keep my hands warm for the minute I need to take the coat off to shoot a stage. My goal is to stay warm with no gloves while still being able to move in the gear I'm wearing when the buzzer goes off.