you can cover with anything you want to, it all has to do with how much money you want to spend. the way it looks I would not lay any tile, that will be costly and it will still be cold. I would lay a free-floating that does not attach to the concrete at all, it just floats, that way if the concrete cracks are moves at all the flooring, will balance out and not crack are a break. that's why I was saying no tile, to much prep wood, floating all the concrete will cost a lot. and they make floating floors that look just like tile, wood, rock anything you want, and you can get it in waterproof, completely all of a rubber type material. with no kind of material that will swell up when it gets any moisture.