I use trail runners when it's spring, the ambient temps are 50+F, and the snow is shallow like that.

In winter while walking in Sierra cement(tm) or deep powder I have a pair of Columbia boots, the kind that's waterproof and insulated, because repeatedly sinking in snow eventually chills and wets out the socks.

There's a variety of options, including the waterproof gaiter approach, for shallow snow and cold. I generally dislike Goretex boots but if continually hiking in conditions such as you describe I'd probably go with a Goretex mid and add gaiters rather than a full boot. Goretex in my usual 3 season temps/conditions is miserable but would probably be tolerable in the cold.

I've had bruised ankles and foot issues trying to use a full boot for 3 season hiking. I suspect the winter boots are okay for me due to the fact that I don't go backpacking in snow, and don't do more than a few miles at a time on snowshoes - and snowshoeing alters my gait and slows me down to the point that I have less bruising around the ankles.

(I've had people argue with me about boot fit - I have zero issues with mid height or low top shoes of the right size, and bruised ankles with full boots that otherwise fit like the low tops. I think in things as important as shoe fit, that you do what works for you and ignore the misguided advice of others who have "normal" feet.)