You gotta have your PS3 hooked up to the internet and log into your PSN account. Otherwise you can't race the seasonals. If you're online, you'll see a seasonal challenge icon in your "My GT World" screen.
@ everyone else:
Since I won so easily on the kart track with a car well below the max PP limit, I wonder if these seasonals are easier than the previous ones. With the previous ones I had to take a car close to the PP limit otherwise I couldn't win (don't like racing on go-kart tracks with "normal" cars anyway). So what do you guys think?
And at all these people saying these seasonals are so much better, in what way have they been changed? With the previous ones you could also select cars that were way below the PP limit, so you could get close racing with those too. I know that I did, always selected cars that were (much) worse than the opposition, well, apart from the go-kart tracks, hehe. The only thing that has been changed is the pay-out, which is just a minor thing really. For me these seasonals are just as good as the previous ones.