It's in the Rattlesnake Island covenant - there are no mosquitoes allowed on the island
Seriously, it is quite rare to encounter a bug like a mosquito - at least on the West side of the island. I can't speak for any other areas, but I hike the mountain every day I'm there, and it is indeed a rare day when a bug "bugs" me.
I'm sure it's a combination of the breeze, and the fact that - at least for Rattlesnake - the sloping terrain gives very little chance for standing water to accumulate long enough for a crop of mosquitoes to get going. It's probably similar on many of the other islands as well.