Ne'er cast a clout till May be out!

As my dear maternal granny frequently reminded me when I was little - not to leave my vest off till May be out.
I never quite understood this. Does it mean till the Month of May is over or indeed till the Hawthorn, also known as May is in bloom?
Well, tomorrow is the last day of May and the Hawthorn tree in my garden is full of May blossom but ...... I am still wearing my vest.
All opinions gratefully received!