What type/size pool are you talking about? You can really go either way. I live in Fresno, our winters don't require traditional pool closeings. The temps don't get cold enough to freeze. What you do will largely depend on your filter/pump system. It would be difficult to clear algae in the spring with an intex cartridge filter.
Here are my plans for the winter. I will use the pool until the water temp is around 60 for a cold plunge with my hot tub. Pool is currently at 88 with my solar. When the temp drops to 60 I will disconect the pump/swcg and drop the water below the skimmer. If you want to keep the pump out you will have to run it on the few evenings that temps drop below freezeing.
It almost as easy to just drain and refill an intex type pool depending on water and chemical balance cost's. It takes about $50 in salt, CYA, and borates to set my pool up.