Do you remember the old days, when they didn't have a non return valve in the washer line ?. This meant that the water mix would drain back into the washer bottle, and if it were heated it would stay warm ready for the next use.
Nowadays, the water stays in the pipe, and as its not warmed, the pipes will freeze up, even though the water in the bottle may be unfrozen, despite the heated washer jets. This is a little bit curious considering the engine is directly beneath them and so presumably there is a fair amount of heat being radiated from it. I just travelled from Leicester to Gomersal tonight, washers were working fine at the beginning but froze within an hour or so.
And there is an exhaust pipe, not a million miles away dumping lots of Kjoules of heat as fast as it can. A shame the heat can't be redirected where it is most needed.
Ken