Five years ago, I landed in the hospital on day 14 of the worst intractable migraine I had ever experienced. They kept me for three days, trying and failing to break through my pain with a cocktail of various medications. I ended up on a morphine drip.
Why cluster headaches are linked to seasonal changes is likely due to the length of the days. How much sunlight there is in a day changes as the seasons shift, making nights shorter and days longer or vice versa.