Tile is conductor of heat while rug is not conductor of heat
When we walk on tiles and we touch the tile with our feet the tile feels colder because it is a good heat conductor and it moves heat rapidly away from our feet skin that is warmer than air temperature. But on the other hand, the rug is a heat insulator and it slows down the flow of the heat which would make it feel warm so our feet do not feel much more colder as it does with the tiles.
