Why is it correct to say, "Summer is the golden season," but not necessary to use "the" when saying, "Winter is exercise season"?
Many kinds of seasons don't require articles:
Any of those five could be put in that sentence, and no article would be required. In that context,
The phrase golden season, however, doesn't fit into that category. Golden season is not the season when we go goldening; it refers to something more abstract and sentimental.
Here, the article is needed, because "twilight season" is not when we go twilighting, but indicates a latter stage of something.
"the" distinguishes the "main" season for an activity.
Summer is the athletics season but spring or autumn may also be athletics seasons whilst winter is rarely regarded as an athletics season.
Other seasons may not refer to the weather seasons and be seasons by virtue of local laws or practice.
The Glorious 12th refers to UK red grouse hunting season - but even that may be the 13th when 12th falls on a Sunday.