The answer to the question, do you need a cold air return vent in each room is no. However it is important that the flow of air in your home is efficient. Basically hot air comes into each room through the hot air registers, usually located under a window. The hot air heats the room and rises to the ceiling pushing cold air towards the floor. This is where your cold air return vents should be located. Cold air is drawn into the vent. Rooms with no cold air return vent and closed doors will have less air circulation.
Hot air coming into the room has no where to go. It creates a positive pressure. Hot air is forced into other rooms with lower pressure. If you do not have a cold air return vent in each room, keep doors open to circulate air.
Our master bedroom does not have a cold air return vent. The room is cold in winter and hot in summer. If we keep our bedroom door closed the variance in temperatures is even greater. We keep the door open all of the time. We looked into installing a cold air return vent in the room which turned out to be impractical.
There was another solution which turned out to be one of the best decisions we could have made. A ceiling fan was the answer. We installed the fan and keep it on at low speed all of the time. The air circulates in the room. The fan pushes hot air from the ceiling towards the floor. Even with the door closed the temperatures are more consistent throughout the room.
The cold air return vent is located just outside the door in the hallway. With the door open and the fan running, air is pushed out of the room towards the door. We have found that it is not perfect. However the temperatures in our bedroom are more consistent and warmer in the winter.
During the summer we have also found significant improvement. Circulate hot air with the fan. This leads to a much more comfortable overall air temperature in our bedroom.