the biggest challenge for catching catfish through the ice is finding them. they don't roam around quite like they do in spring and summer, instead they all bunch up in deep holes and the active fish will circle around in those small areas. inactive fish can be found under sunken trees, and can be caught, but you literally have to drop the bait on their nose for them to bite.
if you have a depth map, take a look around deep water in the 20-30 foot range, and focus on places with steep drops or isolated humps. points are good as well, and as i said earlier, any sunken trees are a good thing to target.
as for baits, all you need to do is downsize. small bits of cutbait, half a nightcrawler, etc. i've had the best success using a small rattle spoon with 3 or 4 waxworms.