My grandparents were farmers - and they've always had breakfast. They had to get up early to milk the cows. I don't know their exact morning routine, but they had breakfast before or after milking the cows in the morning (I would say before milking the cows).
I think breakfast works pretty well for a farmer's livestyle. So I wonder, if this is really the big exception.
And there was always a break in the morning (at 9 o'clock) from a "second breakfast" - or a small lunch break.