There will be almost as many answers as there are photographers. Basically, one needs several different approaches depending on the ambient temperature and your own propensity for getting cold fingers 
Very true and wise words. For instance in a really cold climate gloves become inadequate as one cannot provide enough insulation for the fingers. Sometimes a differential approach can be used depending on the time of exposure.
At normal Fairbanks temperatures in winter (more typical -20 to -40°C), my own preference is a rather conservative/classic Scandinavian approach with windproof cotton shell mittens over 1-3 layers of wool mittens depending on temperature. One of these layers are preferentially of non-compressible ("tovet" for those understanding Norwegian) wool. Needless to say dexterity suffers quite a bit so it becomes necessary to take these off for shorter periods of time to perform needed operations. For how long and when also very much depend on the camera body used. Small consumer bodies like my D5100 will typically require mittens to come off while shooting (but have the advantage of a less heat conducting poly-carbonate exterior), while with my D200 and D7100 basic operations can be performed with mittens on with some effort. Zooming in to 100% with the center button is not possible though. The AF-on button on D7100 and similar bodies can easily be activated with thick mittens, same with the rear wheel and to some degree exposure comp. button and front wheel. There can be an issue with accidental operation of controls, and it can be a bit hard to find the shutter release.
When it becomes necessary to shed the mittens in severe cold,
I find it essential to be able take them on and off very quickly. (Heat will remain in wool layers for some time thus help rewarming hands after a trip out in the cold.) I have personally never found the approach with an inner thin liner glove that is kept while taking off the mittens working, or similar liners with free finger tips. It is just too much friction for me to efficiently slip the mittens on and off quickly, and I want to keep fingers together and freely moving inside the mittens. Often when I start on a ski trip, my thumb gets cold and I can then bring it together with the other fingers to warm up.
I do sometimes change from mittens to a pair of sheep skin lined leather gloves or fleece gloves to operate camera equipment for a shorter time over a 5-10 minute period. During one field trip in on the North Slope of Brooks range I worked for periods of hours at a time day after day only wearing a just pair of fleece gloves (bought in Johannesburg!) at temperature between -20°C and -30°C, but then the rest of my body was
very well insulated to a degree that would not allow exercise for extended periods and I initially accumulated a lot of excess heat skiing up to the site hauling a sled (wearing less layers). In addition I was well adapted to cold as it was towards the end of winter. I would not call that work comfortable though... . The work was photography related so I might get back to that another time.
Normally a glove approach can work for me at temperature down to -5°C to -10°C if I can move a little around and do not have extended waits. For advice on gloves I am probably not the right person to ask as I am wearing something pretty traditional and not anything "high-tech" since mittens is my normal wear.
Also wet vs. dry climate needs to be considered. The breathable membrane approach can of course be nice for a wet climate, but for a dryer really cold climate, the membrane is not breathable enough; one can get condensation/frost buildup, and the fabric can feel very cold as it is a better heat conductor than windproof cotton fabric.
