Lagging is insulation. Nowadays, this comes in the form of polyfoam tubes with a hole down the middle. You simply snap the tube round the pipe to keep it protected from the cold.
An unlagged pipe is bare, and prone to freezing up, bulging and splitting or pushing joints apart when the water expands during the freeze.
You will have to keep a close eye on the problem pipes when the thaw happens, as that is when the leaks, large or small, will become evident.
Hopefully yours has just blocked up a bit with ice and there's been no lasting damage, but it's best to play safe and check things carefully.
Better to discover a leak straight away than have one wake you up at 2am.