The MARC 21 Format for Holdings Data has dealt with some of these issues before (http://www.loc.gov/marc/holdings/hd853855.html)
It uses 21-24 for the seasons, starting with spring, in conjunction with a language code in holdings field 008. Even in English, there is the difficulty of having 2 words for the same season (autumn/fall), which makes round-trip conversions fuzzy. The MARC format tries to allow for publication patterns to predict future issues and has the possibility to spell out which issues are published in field 853 $y. For example, "ps21,22,23,24" would indicate "published in the seasons spring, summer, etc." The rules are not spelled out very clearly and it all depends on implementation in various library systems. In some interpretations, the order could be varied for a southern hemisphere publication, e.g. "ps23,24,21,22", but the format is not clear on whether this pattern should correspond to the volume number or the calendar year. (The time when the volume number increases is handled in 853 $x; some publications change the vol. number in the middle of the year.)
Any format is going to have difficulty with the fact that astronomical winter (or summer in the southern hemisphere) straddles two calendar years and is geographically determined. Publishers can be lax about how they interpret this. One may say winter 2010/2011 one year and winter 2012 the next.
For the format under discussion, it would seem that it depends on what you're trying to achieve. To say the use case is periodicals is too vague. What is to be done with them? If you just want to encode how they designate themselves, that should be straightforward, though the infinite variety of designations and patterns can be mind-boggling. If you want to be able to predict issues based on a pattern, that gets trickier.
John Hostage Authorities and Database Integrity Librarian
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