No a series is a sequence of events that follow on from eachother, seasonal is not a year.
Series does not indicate an ending at all.
There are 4 seasons in a year, not 1.

Also, the old Flash Gordon, King of rocket men etc, were called serials (which ties in with them being a series), and when you talk about books, you might say The Harry Potter series of books.
Even in comics you have mini series an ongoing series!

Series makes a lot more sense.