Weather might cause performance issues, but I don't see why it should - plenty of games have similar scope and manage it. GTA4 had a decent cycle of conditions, and that was a while back now.
But time of day transitions won't have any effect on performance - they're already using realtime lighting, so moving that light source around isn't going to add or remove anything. Obviously they'd need to also have a skybox transition, but that's just a texture so it shouldn't cause any problems.
Although I guess with a changing ToD, they'd need to include dynamic lights on the cars and around the tracks too, which is where the real performance hit would come into play. That graphic quality, crazy amounts of shaders on each car PLUS light sources flying around, casting shadows all over the place? Could be nasty.
I hope they can implement it though, because it would be nice to have a range of experiences available for each track.