although "should" in this case just means that that's the only way to get this right with Zotero at this point. I'm a bit torn whether more generally that info should actually be in the issue or the date field, I can see arguments for both.
And, obviously, Zotero's date field should allow date ranges either way (and everyone agrees that it should). Will still take some time, though.

You can enter “Summer 2004” or similar in the Date field. Zotero recognizes seasons.

Oh in that case, could you describe exactly your situation for @emilianoeheyns ?

I'm unable to make it display season for journal articles with CMOS author-date style. I've tried putting "Winter 2017" in the date field for this particular citation.

With note-style there doesn't seem to be a problem. I get this:
Author. “Title.” Journal 31, no. 1 (Winter 2017): 117–40.

But with Author-Date I just get this:
Author. 2017. “Title.” Journal 31 (1):117–40.

According to CMOS 17th "15.9: Author-date references—examples and variations", all information should be included, and it should there display like this:
Author. 2017. “Title.” Journal 31, no. 1 (Winter): 117–40.

Is there a way to get around this?

Not sure I fully understand what you mean. It appears it does test for presence of date parts in some cases, as with Notes-style per the example above?

For Author-Date-style it does show date or season if either volume or issue is missing (apart from the case of volume and season present, then it only displays the volume no. I've tested for all the examples and this is what I get:


Author-Date (volume no. + season present, issue no. not present) – does not display season:

[Author]. 2016. "[Title]." [Journal name] 18: 191–218.


Author-Date (volume no. + month present, issue no. not present) – does display month:

[Author]. 2016. "[Title]." [Journal name] 18 (December): 191–218.


Author-Date (issue and season present, volume no. not present) – does display season:

[Author]. 2016. "[Title]." [Journal name], no. 1 (Winter): 191–218.


Author-Date (issue and month present, volume no. not present) – does display month:

[Author]. 2016. "[Title]." [Journal name], no. 1 (December): 191–218.


Author-Date (volume, issue and season present) – does not display season:

[Author]. 2016. "[Title]." [Journal name] 18 (1): 191–218.


Author-Date (volume, issue and month present) – does not display month:

[Author]. 2016. "[Title]." [Journal name] 18 (1): 191–218.

Just reporting that I also get Better BibTeX export errors for any date with a season in it, whether it precedes or follows the year. The year itself is not output into the (BBT generated) .bib file, but the standard BibTeX export will output the year without the season.

For example, the record which yields the Chicago full-note style citation:

Ansoff, H. Igor. ‘Managing Strategic Surprise by Response to Weak Signals’. California Management Review 18, no. 2 (Winter 1975): 21–33.

yields the following BBT output (May 15 2021 update):


@article{ansoff75mssrws,
title = {Managing strategic surprise by response to weak signals},
author = {Ansoff, H. Igor},
volume = {18},
pages = {21--33},
issn = {0008-1256},
journal = {California Management Review},
number = {2}
}
% == BibTeX quality report for ansoff75mssrws:
% Missing required field 'year'
% ? Unused autoJournalAbbreviation: Calif. Manage. Rev.
% ? Unused journalAbbreviation: Calif. Manage. Rev.


This occurs whether the date field is "Winter 1975" or "1975 Winter", and the Chicago output will always do "(Winter 1975)" no matter the order of season and year.

If one uses Better BibLaTeX output, this is rendered as:


@article{ansoff75mssrws,
title = {Managing strategic surprise by response to weak signals},
author = {Ansoff, H. Igor},
date = {1975-24},
journaltitle = {California Management Review},
shortjournal = {Calif. Manage. Rev.},
volume = {18},
pages = {21--33},
issn = {0008-1256},
number = {2}
}
.

Note the date, which I think is citeproc's way of rendering 1975 Winter. This also occurs when entered either as "season year" or "year season".

I'm assuming that treating the season as a more complex form of "month" will not work -- by which I mean: "month = {Winter}" is output, as opposed to the standard three-letter abbreviations without double quotes in standard BibTeX. (I know it's bad BibTeX style, but I'm trying to kludge it to work...).

I guess some insight into the plan for dealing with "Season Year" date entries in the next version would be handy, before I go ahead and add "Issued: Year Season" into the Extra field of all of these records...

1975-24 is not citeproc though, it is ISO 8601, and for biblatex, date = {1975-24} is correct (see https://tex.stackexchange.com/a/396619) and this is the only way you get properly translated seasons.

5.4.12 should be out in 10 minutes and exports season dates for bibtex.

5.4.13 is out.

The .bib file contains error messages such as that shown above ("missing required field year"). It seems that the season entry confused the parser and dropped the year on output, which is undesirable output (i.e., lost data).

Ah, those; that is BBT's quality report. They're not errors perse, and they're not error messages reporting on BBT itself; I was thrown off thinking BBT was misbehaving.

A quick look through the (standard Better BibTeX output) .bib file shows the year now being picked up and the season rendered as "month = {winter}", with upper-case "W" in Zotero converted to lower case "w" in the .bib file. Other records with seasons similarly, with the lower-case first letter.

That's just because of this. The choice is somewhat arbitrary, since I don't know where the term will show up in the bibliography (where a leading capital would be appropriate or not). It's not really a direct translation of the term; BBT has a fairly extensive date parser, and the resulting structure gets written back out in a form most appropriate for the target format. Date parsing is exactly the same for better bibtex and biblatex, the exporter just didn't do anything with the season-date case for bibtex; this is now fixed.

So, this now works as per the advice given in the stackexchange post shown above (I knew it was bad BibTeX style to use "month = {Season}" since it won't translate to other languages), but I was intrigued to see the stackexchangers suggesting the same crude kludge! I guess that's what happens after 30 years of LaTeX/BibTeX ;-)

I just went by what I found there, so it's not that much of a coincedence :)

Given that this now seems fixed, is there still a need to open an issue on Git?

No, if this satisfies you, this is fine. I have a test case to prevent regressions, and I have confirmation, so I'm all good.

Ah, I see. But I can also see that the UK and Australia, for example, will also need an "autumn" entry in the case 'season' selector, because we speak correct English ;-)

this is something I'd like to discuss on github. I have my support infra there, and access to people who know the arcana of bibtex (which is not necessarily me).