the perfect way to fish for cutthroat is with flies. Anyone up for fish on the dry fly in early winter? Very small chironomids (midges) mayflies stone flies all hatch when conditions are right and the cutties rise to them. Nymphs work too of course. Cutthroat also take various bait fish through winter - salmon alevin and fry, various little minnows sculpins etc. Think small bait fish patterns like egg and I, tied down mylar minnow, wooly bugger and various muddler style patterns are all productive. Most of the time I fish with a floating line. Weighted patterns can get you as deep as you need most of the time.
If you really don't want or can't use fly gear, small spinners (like a #1 or #2) and small spoons catch fish. Never used them for trout but little jigs in darker colours should look like sculpins.White will look like lighter colour fish or scraps of rotted salmon - which the fish eat. he often taste just like that in late fall and early winter. Rubber or plastic eggs do well while salmon eggs are still available to the fish.