We've a 15mm plastic mains water pipe on an outside wall.

I haven't got around to lagging it yet so as a precaution i've been
turning it's supply off in the evening and had been expecting to open it
up and find it frozen.

Having had no bother and it being zero and under recently around these
parts i'm wondering at what sort of temperature you'd actually get freezing?

I realise that rather than debating this, a better use of my time would
be to go and get some lagging!