There are relatively few cases of true synonyms in English (or any language). There are subtle differences in meaning, register, etc that are recognized by native speakers.
So I'd prefer to stick to concepts that actually do mean something, where "synonym" is two words that have the same primary functional meaning. Splitting hairs over whether autumn is "cozier" than fall does not change the fact that they are synonyms by any reasonable definition, or change the point that English has a hugely larger number of synonyms than any other language, for certain historical reasons.