Wait a second.
I seem to have noticed something. When I go to Practice mode in GT Life, select Nürburing with dynamic time/weather, I can somehow choose whether of not I want to begin with weather or not. If I put rain tires on my car before I select the track, the track will be dry. And it will start off with rain if I choose any other tires.
EDIT: Disregard my post. After some testing, I found out it's random, which is stupid. 👎
