Irrelevant for me personally since I have central air, but back when I had to use window units, I never installed prior to June because you just had way too many cold outbreaks before then and an AC window unit lets a lot of cold air in, so you end up having to turn heat on when you might not have otherwise.
Try seeing how cold your room gets if you have a window unit in there with the heat off and you get a wheel 'o 'rhea for 3 days at 44F.