The downstairs of my house is at ground level and sits on concrete (no basement). The flooring is tile and during the winter it gets very cold down there, in part because the tile floor is just above the concrete slab.

What suggestions would anyone have on another type of flooring that I can have installed that might keep the room warmer? I would like hardwood floors but I was told that you can't put hardwood floors above concrete, unless a) plywood is installed first or b) I use engineered wood.

Is this true?

Yes with the hardwood needing a nailing surface, it can't be directly on concrete. A plywood subfloor would not only give you a nailing surface but also some thermal break between the concrete and floor, not bad idea. Carpet with padding would likely give you the best thermal barrier.

Thanks Ballengerb1. How thick is generally a plywood subfloor and would that cause the floor to be higher than it is now. If so, it probably won't be a problem as we would do it throughout, but what are your experiences in how people handle that?

Yes you will be raising the floor by over an inch. You hardwood is usually 3/4" and I'd use the same thickness for the ply. It will require doors to be cut and any cabinets or counters to be raised. It would also affect plumbing, primarily the toilet if there is one on this level.