I was trying to think through this for a bit, and I can not provide a direct answer.
Remember that people make their own connotations of words. I can equate this in English to saying "wake me up when September ends"; September in itself does not pose any meaning here, except it means something to the song-writer (in this case the reminder of a person).
For here, the songwriter uses the evening glow (夕焼け) to represent his emotions in the song, and perhaps this is subjective: is this evening glow visible in the winter as much? I can only say this much. Further, based on the song's message (I would assume you would better understand), is there a symbolic reason to remove 冬?
However...
Alternatively, this may be a frivolous question to ask to begin with. Based on the cadence of the song, fitting in 冬 would sound weird. Given that Japanese tends to cut off sentences and shorten words, maybe he was implying all the seasons (the typical word used), and just expected the listener to put them all together. I note that a transcription of the song (likely made by a native speaker) does not correspond with the original video I saw, as it does not make 春秋冬 into a single word, but instead makes the word trail off, and then continues with the song:
ああ春夏秋...と
We can always overcomplicate a songwriter's intention, but perhaps he was implying 春夏秋冬, but just could not fit it in with the rhythm of the song. For you, it might be best to just not think the exclusion of 冬 as meaning anything; it does not seem to be an important part of the song anyway, as evoking the seasons is very common in Japanese songs.
P/s. The song was released on Feb 3, 1989 (it was winter in Japan, right?)
– HK boy Mar 10 '23 at 08:37