While stationed in Anchorage as an Airborne Infantrymen, we were issued two types of cold weather mittens.
The Artic mitten had no fingers, just a thumb and was covered with fur on the backs to warm tour face. Used when it was f***** cold and not a big requirement for manual dexterity.
The trigger finger mitten, similar to what you’ve shown, had a separate finger for (the trigger) as well as the thumb. The trigger finger sleeve could be folded back and tucked into a strap to keep it out of the way and worn like regular mittens. The palms were covered with a supple leather to give a better grip on a weapon. We actually used the M16trigger guard as it was designed, to fold down along the hand guard.
Most of us used a good lined 5 fingered glove for most everyday use. The Artic mittens were great when it got really cold and standing around (good training) was the the order of the day.
This was back in the mid to late 70s and we were still using the same equipment that was designed in the 40s. We hosted some Canadians once, but it was during the summer, so we didn’t get to see their cold weather gear.
Hope this helps.
Ken