The green is not necessarily from not covering properly--many of us never cover our pools. The green is from letting the chlorine get too low for too long, and then the bacteria in the outbreak can break all the CYA down, which is why it's gone over the winter. Unfortunately, one of the byproducts formed when this happens is ammonia, which then takes a whole LOT of chlorine to break down.

Do you shock your pool before closing in the fall? Have you tried adding polyquat (the only algaecide we really advocate here) during the closing process? Do you have a way to add bleach during the winter, even if you have to stir it around with a boat paddle or something? All of those things will help prevent the green. Also, you might want to consider opening a little earlier, before the water has a way to warm up and let algae start growing.