I don't know if it's related, but "hydref/Hydref" sounds a lot like "hidro-", which is a Greek rooted morpheme meaning water, as you surely know. Well, that at least serves as a memory aid, if we think that not only autumn is the wettest season, but October is the month with the most precipitation in Wales.
GCP suggests it comes from "Hydd+bref" (Stag/Hart+Bleat/Low) refering to when a the male deer
would bleat for their mates. It also gives this from a dictionary by a W.Owen Pughe
"1803 P, hydrev, the ingathering, or harvest season; autumn; October.
id (The same as)., hyddvrev, the rutting of deer; rutting season; october."
The notes -- https://www.duolingo.com/skill/cy/Months -- state:
yr hydref - autumn
mis Hydref - October
The mis is sometimes dropped when the context is very clear or when used with dates (covered later in the course). Apart from when using dates, it is best to use the mis, and this is what Duo does.
((My two cents: Also, it looks as tho the season can start with a lowercase "h" but the month, a proper noun, can't.))