Colocasia esculenta 'Magic', or Caladium bicolor of one cultivar or another, but definitely not Coleus.
The tubers, so long as they're dry and not mooshy in any places, will winter just fine - treat them the same way you would tulips, irises, or other perennial bulbs that you'd take in for the winter (store in a cool, dry place with not too much light.)
You can absolutely keep them as houseplants provided that they've still got leaves when you bring them in. If they've dropped their leaves, they've entered their dormant period, and breaking that dormancy early isn't very good for the plants. If they're Caladium, they naturally take a rest in the fall, even here where they're native. If they're Colocasia, they go dormant when the tubers are nice and mature (it's how you know when to harvest them for eating.)