Hooray! I get to show off my knowledge!
"Cast ne'er a clout 'til May is out" doesn't mean you have to wait until the end of May before abandoning your winter clothes, but actually refers to May blossom - the small white flowers that fill hedgerows, usually in early May - known to its friends simply as May. So "May is out" means stay wrapped up until you see those flowers.

As their appearance is correlated with Spring's arrival, it's not bad advice.
( Olembe Refuses to write in this space, Thu 3 Jul 2008, 18:08, Reply)