The first day of spring is traditional.
The Middle of Spring relies on 'Cross-Quarter-Days' to define the start of the seasons.
One of the blogs I read is the 'Bad Astronomy Blog' and Phil Plait usually has a post about the Equinox each time it happens. This post: 'Fake Equinox' has a link to an earlier post 'Bad Seasons' which talks about starting the seasons on the cross-quarter days.
Well when I read that I thought, "Wow that sounds familiar!" and this is the web page that makes the same point 'Another Way Of Looking At When The Seasons Start'.
I first wrote the web page back in 2000 and I do note that Phil Plait wrote his in the late 1990's.