Yes, temporada is season for something, like hunting season etc. estação is season like summer, autumn, winter or spring. I at least think.
No one has properly answered this question in 4 years. I guess that is on the moderators.
They both work. But as you dont have any extra information, it sounds better to omit the article (Outono não é uma estação muito chuvosa). But no problem to use that.
Is it unusual for words ending in ão to be feminine? Or is it fairly common?