The correct version is " Ne'er cast a cloot 'til the May be oot" (Yes, you've guessed it, that's a Scots saying!!
It is NOT "Ne'er cast a clout 'til May be out!" (This is utterly meaningless - sorry BBC, that is a dig at some of your presenters)
Why? Well, the original means 'never cast off your (winter) clothes until the May blossom (ie the hawthorn blossom) appears on the trees. - a wise and sensible precaution in this fickle climate of ours!
A 'cloot', rhyming with 'loot', in Scots is a cloth (ie clothing) - whereas a 'clout', rhyming with 'out', is commonly perceived as a belt round the ear delivered by an angry parent (when such things were not politically incorrect, of course!) Hence the anglicised version of the saying is rendered utterly meaningless. OK, there is less of a problem with the confusion between the month of May and the May blossom - these tend to be contemporaneous anyway!
Please, please, if non-Scots are to quote Scots sayings, afford us the respect of getting them right! (or has the BBC got rid of its pronunciation unit altogether?)