Had the same problem with headlamp washers stuck open, I noticed the issue after a 30 min roundtrip this morning. I called my Lexus service centre and it was explained to me that this happens because of pressure build up due to the low temperatures; they said there are no actual electric motor operating the washers, it apparently works with pressure, and that I was the fourth person calling about this issue. I wasn't initially happy with their response suggesting that this is normal during cold weather. The washers slowly retracted after 1-2 hours on their own, at least it seems they don't stay up permanently during cold weather, still not a great design in my opinion, or maybe just a wrong choice of screenwash as suggested here. Interestingly it appears that my washers retracted as the car was cooling down after the journey, so I am totally confused about the cause/effect relationship here.