Sleeping on the floor is normal for many cultures, mang.
All you have to do is make sure that you are insulated from the floor, by a blanket or cushion or whatever. Otherwise you will catch a cold that won't get any better until you stop sleeping like that. I've heard that sleeping on cold surfaces, especially stone, can lead to bladder infections and enuresis (= pissing on yourself).
If something is causing the floor to be constantly cooled, like airflow underneath the room (ie mobile home or room over garage), or if you're right on the foundation, it will basically be a big heatsink, and your body will spend all of its energy trying to heat the world outside. That's what gives you the cold. If the bedding underneath you never seems to warm up, then you need more.
If you have a sleeping bag, you could try unfolding it and lying on top of that, with a comforter above you. But definitely don't sleep in the bag closed up. Your sweat will collect and that's never good.