If his issue gloves are large enough he could try a pair of these underneath as liners. They are windproof plus a 2nd layer would help create a warm air pocket. The thermal reflective bit I thought might help. I ordered a set today to wear as liners under a set of fleece gloves when hiking. Drop the heavy gloves and still have something to use while shooting pics, or guns.

https://www.columbia.com/mens-wind-b...ve-SM9481.html

Plenty of other companies out there that make windproof gloves. Just a matter of fit.