“Shed not a clout till may be out…”
It’s not an instruction to keep your coat on until June; it’s telling you that you can take your cardigan off once the may is in blossom, which has been known to happen as early as April.
May blossom is the flower of the hawthorn, which is a traditional marker tree, used to mark boundaries, paths and gateways. In Southwick Country Park, there is hawthorn in the oldest boundary hedges, and both of the old footpaths out of the park are marked with hawthorn.
Hawthorn has been significant in Britain’s myths and legends for at least as far back as written records go and probably much further. In some stories hawthorn trees mark the gateway into the worlds of faeries and giants, or between this world and the underworld.
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1. A hawthorn tree marking an ancient path at Bratton Camp;
2. stamens on hawthorn blossom.
Perhaps because gateways look both ways, may blossom seems always to have been viewed from two different perspectives. Outside, it marks the boundary between winter and spring, and it has been used for millennia to celebrate and garland May festivals, a symbol of rebirth and growth. Inside, it is taboo: even today it is believed that to bring may blossom into a house invites disease and death in from some other world.
Southwick Country Park Nature Reserve 
I remember last year some of your may blossom was tinged with pink, I noticed it in my garden too. This year blossom seems to be pure white, as it should be!