The only time I won't fish a jig deep is during the spawn periods. But in winter you do not always have to go "deep" with a jig or any bait for that matter. Depending on the body of water subtle little drops, say a drop from 2 feet to 6 feet can hold plenty of fish depending on how cold it gets in the winter. One of the lakes I fish up here has a max depth of 10' and get iced over four months of the year. Yet the best area I have found to fish in the lake is a subtle little drop that goes from 2' to 4' with some rock. If you can find a small overlooked drop with some wood or rock on it, it can be a sweet spot.
And during a warmer spell fish will move from these small drops (say in 15' of water or less) that are close to shore, up to the shallows and under docks, along rip rap, and under wood. Whenever they can move up shallow and get warm, they will. You can hit them in a fury in the last half of the day if it was significantly warmer than the water temp.
I won a tournament last spring or the spring before (can't remember lol) with water temps ranging from 41-43* by pitching a light jig into a foot of water or less. They key was the lovely bluebird skies, slick flat water, and 55-60* temps in the sun. I had a limit for 13 pounds while second was 2 fish for 6 pounds. The entire field was fishing jigs, grubs, and jerkbaits in deep water.