However, factually, lots of catfish are taken through the ice each year, and some species, especially Blue Catfish and Channel Catfish, are actually fairly eager biters in the cold water. So, the issue, really is one of first deciding to get yourself outside, and do some icefishing, and then, of setting up your rig to do the job.
There appear to be two "schools" of icefishing thought (pardon the pun), where cats are concerned. The original, old-school, lazy one, is that of finding a nice, comfy-looking spot that at least appears to be a likely hookup point for a decent fish, drilling a hole in the ice, and sitting next to your fire tub, or in your "fish house" (tent on the ice), and enjoying the outing, as much as the catching of any fish that might happen by. The second way of seeing things, is that each outing is a competition for a record volume catch, and as such, the fish must be militarily tracked down, cornered and exposed, and then taken by the bucketload.
For sure, a scientific and tactically-planned approach to your outing will probably yield the most fish. However, this viewpoint also requires the most equipment, as its proponents work among perhaps two dozen holes in the ice, and track the fish from spot to spot with sonar fish finders, while racing to the next hole on snowmobiles, and attempting to "head off" the fish at each hole as they move.
While the top producers in this "sport" can bag over forty fish an hour, there is still something to be said for skill and patience, in selecting your spot, baiting up, and playing on a level field, without a pile of electronics and machines to remove all hope for the catfish. After all, the sport of fishing includes both finding the fish, and the actual fight, once you set your hook. It just takes more nerve and determination, on the ice.
Regardless of your approach, you'll need the usual sturdy gear for cats - a strong rod with a decent spinning or star-drag reel, good braided or monofilament line, proper terminal rigging, and some nice, stinky bait. If you want to use a more conventional icefishing rig, a flag float or tip-rig will work OK, but remember the size of the fish you are after - these kitties are going to be a tough fight, and handling them without a rod is even tougher.
As far as bait goes, smell is even more important in cold water, than in the warm months, as the scent doesn't spread as fast, or present as strongly in the water, so the more potent the bait, the better. Small dead fish are still an excellent choice, especially for Blue cats. Puncturing the bait, or dipping it in some stinky adjunct, may be another possible improvement, to really get the scent going. Some anglers feel that the color of the bait is of importance in icefishing for cats, due to the reduced spread of scent in the cold, but in deep water, it's quite dark, and catfish are known to have weak eyesight, so the importance of this factor is open for discussion.
In nature, cats eat fairly dull-colored, smelly food, so, give 'em what they want. With smelly, natural bait, the only other issue is where to fish it, assuming the fish will take it, if they find it.
Of all of the places one might go in search of a big catfish, rivers seem to be the waterways that come to mind, when we think of these big, whiskered lunkers, probably because of the huge amount of lore surrounding catfish and the rivers of the American South. But then, the lore is there for a reason - the biggest cats in the world generally live in rivers, and in the case of North America, the rivers in which cats can be found are plentiful, with river-dwelling cats found in most areas of North America, except for the extreme North. The only thing that changes, is the size and species of cats that live there. Depending on the locale in which you are fishing, the species you find might be Channel Cats, Blue Cats or Flatheads. Blues and Channel Cats are fairly similar in habits, but Flatties have their own way about them, in certain respects.
Virtually all cats prefer darker conditions, and so, tend to move toward deeper water, with lots of structure or relief on the bottom. Because of their penchant for low-light conditions, nightfall is far and away the best time to pursue them. River fishing for cats adds a consideration in the form of the current, which can be your friend or foe, depending on how you approach things.
Generally, cats like a solid current flow, making rivers an optimum choice for catfishing. So, working with the current is the best bet. Since the current will tend to push a light bait up, as the line tugs at it, if you're casting a line, you'll need to choose a heavy, sinking bait, or use a sufficient sinker weight to get the bait down to the fish. Alternatively, jug fishing rigs or trotlines are effective at covering lots of water, and keeping baits in the action zone.
Trotlines are a line which is stretched across a span of the waterway, and secured on both ends. Along this line are spaced a number of "drops" (20 - 70 or more), which are lengths of fishing line secured to the main trotline, with a hook (often two) baited along their length. A heavy trotline will keep the centre drops down deep in the channel, and will follow the bottom progressively up as it moves towards shore at its ends, keeping all the drops near the bottom, and the fish.
Jugfishing uses a number of individual floats (jugs), each with a baited drop suspended beneath it. Drops of differing lengths can be used on several jugs, to cover a great deal of water, at every possible depth, and can have different baits deployed, too.
If you are fishing with a rod and reel, make sure your gear is strong and appropriate to the size and strength of the very powerful fish you are after. Fishing from shore, a sliding ledger, or slipweight, is a top choice for weighting a bait, without creating a stop between the bait and the rod end.