I think that this is right.
Feb, Mar, Apr is Season 1
May, Jun, July is Season 2
Aug, Sep, Oct is Season 3
Nov, Dec, Jan is Season 4
Note that for a given year, 2009 for example, Season 4 has Jan 2009 and Nov and Dec 2009. The season is not Nov Dec 2009 and Jan 2010. January 2010 would be out of the 2010 use year.