Why is the airflow in airline cabins downwards?
Temperature stratification is a vexing problem on lots of airliners.  The big challenge is you need a distribution system that is effective when cooling (on the ground and at low altitude when the weather is hot) and heating (as soon as the outside temperature drops to the point where there is a net heat loss that can't be made up by passenger body heat, the ECS will be producing inflow that is warmer than ambient).  At cruise where the  outside temperature is generally -10 to -40C, you are in heating mode, where inflow temperature is above ambient.
The objective is to get a circulation going (air falling along the side walls, and rising at the center aisle) to keep the air mixed and prevent temperature stratification in the small space, with the added factor of a large heat emission from the passengers to cope with. Distribution systems strive to do this.

So you would think that most of the time, you want the air coming in at the floor so there is a natural convective circulation favoring heat from below (most of the time incoming air is warmer than ambient).  Problem is, you have the heat of the passengers, which is significant, rising into the ceiling.  You generally want to measure temperature for regulation purposes at somewhere around passenger head level, and if the heat comes in at the floor, there is a tendency for heavy stratification as the sensor is remote from the incoming heat source and it creates a very long response loop (sense, adjust, wait for the result, adjust again, etc.).
The CRJ200 suffers badly from this problem because the airflow is from Dado panels along the sides at the floor like a home heating system (a design carryover from the Challenger corporate jet, which had different distribution requirements).  The temperature sensor is up by the overhead bin.  When the sensor called for more cooling, or even just less heat, the Environmental Control System would dump in all kinds of cold air, which didn't want to rise being colder than ambient, so it would have to, in effect, fill the bottom of the cabin space with cold air (or really, less hot air) until the &quot;coldness&quot; reached the sensor up at the bin.  Anyone who's ridden in the CRJ200 knows well the cold feet problem with that airplane, even at altitude where it's -30 outside.  What helped a lot was moving the sensor down near the floor to the inflow region to reduce the response loop, and a modification was created to do that which was quite effective, but few airlines bothered with it and having the sensor near the floor is generally suboptimal from a design perspective.
On the later CRJ versions they went with the more common airliner arrangement.  Air is injected up at the overhead bins somewhere and most of it is shot at the sidewall panels, to get a waterfall sort of flow down the sidewall panels, inboard along the floor and up the center aisle(s) (some air may also be injected into the space between the bins to prevent stagnation there).  This works reasonably well even when in heating mode where the air being injected down is warmer than ambient, and allows the temperature sensor to be in a good location with a reasonably short response loop, so variations of this type of distribution system are the most common.