I don't think it's too early, but I'm one of nature's larks so am usually awake by 6.
I accept that other people aren't though, and I wouldn't cut my grass before 9, or maybe 8.30. I'd love to do it first thing, at 7, say, so I could do it before going to work!
I think it's difficult at this time of year, as grass yellows so quickly if you cut it while it's in the sun. Unless I faff about all day, doing different bits of the garden at different times, I can only really do it before 9 or after 7, and after 7 people may well have young children trying to sleep.