I rode a mare once with an unsolved eye problem. If is was cloudy and rainy, she was 110%, but as soon as it was sunny she was squinty, sluggish and just wanted to stand around with her head cradled, or rested on something.
If it was anything like the migranes I get (which are entirely occular, I have no noise triggers) then I can understand the feeling of how bad the occular nerve aches and you just want to rest your head in the dark.
So yes, horses can get "headaches" - this mares were greatly improved with steroidal, anti-inflammatory eye drops, which you may want to suggest to your friend if the mare appears squinty, or has excess discharge from her eyes that wont resolve with any amount of duct clearing.
They say money doesn't buy happiness -- well happiness doesn't buy horses!