While switching between leveling one of my alts on the LIVE server and testing a new build on the PTS server i noticed that both always had the same time of day and weather whenever i switched between the two.
So i fired up both at the same time and sure enough, time of day and weather are exactly the same between both clients, regardless of what character you play and where in the world you are!
I teleported around to see if the weather or daytime changed, but it stays universal to both clients.
When it rains at midnight in Craglorn on PTS, it's also a rainy midnight in Auridon on LIVE ...
;-)