I do something similar til Rod, using an ultra thin silk or wool glove liner first, and then wear something heavier over that. The heavy mitten/glove varies depending on how cold it is.

For example, I'll wear a thin liner like this:

And then a fingerless glove/mitten combo like this over it:

The thin liner lets me feel what I'm doing since they stick out of the gloves cut off finger tips. When it gets colder, I flip the mitten part over my fingers.

Or if it's even colder, then I'll wear a heavier mitten as an outer layer, and only remove it just when I'm ready to shoot with the inner liner on:

Fwiw, I am absolutely not a Lowe Alpine agent, but I happened to find all the things I needed to illustrate in one place.