It's one of the oldest ones in the book - but there is a certain amount of debate as to what exactly it means.
The clouting bit is clear enough: it's all to do with warm clothing. A 'clout' is an olde-Englishe word for 'cloth' - so 'casting' (throwing) a 'clout' (cloth, or coat) means taking off your coat.
So you might interpret it as warning you against thinking that just because there's a spate of warm weather going on early in the year, you can go ahead and act like it's summer: chances are we've got more cold weather on the way and that coat will be going back on.
In gardening terms, this means you can't be absolutely sure there won't yet be a late frost - even if it is 25°C, hasn't rained in weeks and everyone's heading like lemmings to the seaside.
But what about the 'May is out' bit? Some say it means you shouldn't lower your guard (or your horticultural fleece) until the beginning of June. But, it has also been pointed out, it could refer to the old word for hawthorn - still known as 'may' by my mum, who used to eat the leaves when she were a nipper. She called it 'bread and cheese', but don't try it - it's horrible.
Well guess what.
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So to continue my selfless pursuit of research and truth in the services of English etymology: this is by way of marking your card. If there is no further frost from this point forward, I think we can safely say that 'may' in the saying refers to the hawthorn.
If however I have been entirely duped and bamboozled and my new potatoes - now already at the earthing-up stage and about as vulnerable to frost as it's possible to be - are clobbered to black slime by a perfectly normal May frost, I think we can probably conclude that the May in question is the month.
Actually, for completeness, I could do with some fellow researchers a bit further north: is there anyone not quite as close to the south coast as I am with may in blossom at the moment? Let me know and we'll see if you get caught short by a late frost too. Citizen science - it ain't just the Natural History Museum at it, you know.
Oh, and I hope you all had a very happy Easter, by the way!