The following usually gives me a little more confidence when I'm trying to catch a Carp or two in the depths of winter in the waters that I fish. Although you will usually find me fishing moving waters for fish like Chub, roach or pike or even the occasional barbel when the winter finally sets in simply because on moving water these fish will be needing to replenish their energy a lot more than their Stillwater brethren.
1. If the temperatures have been steadily rising or have remained steady for a few days and the water temperature is at least between 4 to 7 degrees C.
Falling water temperatures are a definate no no for me when I'm after Carp.
2. Carp often follow the wind when the surface Layers contain suspended or floating food so fishing into a wind can be very productive a lot of the time; however during the depths of winter they will also look for any sheltered areas which are protected from biting cold winds and where the water can often be a degree or two warmer.
3. I also tend to use smaller meaty or Spicey smelling baits and slightly lighter lines and hook sizes.
4. Finding any underwater springs that may be in a water (which often stay at the same temperatures throughout the whole year) or any deep holes or gullies, can often mean the difference between me having a blank or catching a Carp in the depths of winter.
5. Remember that most fish tend to shoal much tighter in the winter and move around a lot less so be prepared to search more for your fish.
6. On moving waters in exceptionally cold weather fish are much less inclined to chase a bait washing downstream especially in near flood conditions when the flow is much faster so if you are struggling for a bite then also try a method that can present your bait a little slower (e.g. stret pegging or legering or rolling a bait more slowly along the bottom etc.)
I would be inclined to look for a venue where the fish see some bait all year, that way they still have some incentive to feed.
I was on one of linear's waters last autumn and one of the bailiffs was hypothesising about the way the carp's behaviour had seemed to change in the autumn... so whereas a few years back, the fish would feed quite hard in autumn (because the winter would be a period with much less natural food available), now they would not bother so much because the waters are fished all year round and bait is always available to them. And they're getting caught too. So if the fishery is still seeing some bait going in, chances are the carp will still be feeding, albeit less enthusiastically than in summer.
That said, the one tip I'd offer is don't ignore bread as a bait during the winter. It doesn't have the richness of some other baits and might be a bit more appealing during the winter months, plus the small fish activity is much less (so they're not smashing it to pieces the way they would be in summer)
Generally I don't feed, if I do it's only a single piece of corn, meat. bread normally popped up is another choice.
Only feed if you detect fish are in the swim, to find fish cast around with a small bomb, 1/4 ounce for me. Cast keeping a tight line to the bomb and watch for liners.
I typically don't have an hooklength on when I'm searching for fish and leave casts no more than 3 or 4 minutes, if liners are detected I start with just the hook bait and feed nothing until I see how the fish react. This is on commercials.