Food coloring will not degrade the quality of the milk in any way, and as long as you use it sparingly, it will not change the taste. The expiration date will remain the same.
As long as you don't have a problem with it, anyone would have an aversion to light green milk. It's an ingenious idea actually.
Alternately, you could obtain your own minifridge to keep in your room. One large enough to hold a gallon. If not, buy the half gallons or the quarts, just buy them more frequently.