You aren't going to have warmth with cut-off finger tips. Mittens are designed to keep warmth because the fingers stay close to each other and give body heat to each other. Having no finger tips would be counter productive.
If you can get the right design tactical glove you shouldn't have any problem keeping your fingers warm while keeping dexterity. You can even place a thin cotton liner in your glove if you decide to cut off the trigger finger in the winter. Liners like that are less than $3 a pair. A good pair of tactical gloves can run you up to $100. At that kind of price (or even half that) you can expect to have a lot of tactility with your trigger finger. Check out some of Line of Fire's gloves. Outdoor Research has good cold weather gloves. Ansell Hawkeye has a good finger design in a few of their gloves as well as Camelbak and HWI.
Source: Tactical Gloves
website with a lot of information on a variety of gloves. Nothing about outdoor research though, you'll have to go to their website for information on that.