I use a shooting glove, but for this discussion it doesn't matter.
I use a muff with Hot Hands warmers inside to keep my hands warm while sitting & waiting. I keep my shooting glove on & stuff both hands into the muff, & they stay toasty warm!
But, when I'm going to and from a hunting spot, I don't have the shooting glove on-I put on a pair of thin deerskin gloves for the walk in or out. While sitting, I stuff them inside of my shirt to keep them warm.
I practice shooting with those, as well as my normal shooting glove, and I'm now used to shooting with both. The shooting glove is thicker and I feel the string less, but for the one shot that I might take with the deerskin glove, it's definitely doable!