Question

Room heaters in winter are placed on the floor and not mounted on the wall like air conditioners

Answer 1

The density of air depends upon the temperature. If the density of air is high then it will settle in the bottom and if it is less dense and it will move upwards.
If the heater is placed on height then the air will not fill the bottom of the room. Hence, heater is placed near the floor because the air currents move upwards so the hot air fills up the whole room.

Similarly if the air conditioner is placed near the ceiling because it gives out cool air. If it is placed near the floor then it will fill just the bottom of the room with cool air. So it is placed near the ceiling because the cool ( high density ) air tends to settle downwards.

Answer 2

Air conditioners are mounted on the wall because the hot air being less dense is gathered upward while cold air is heavy and is at the surface..Thats why room heaters are placed on floor not on wall