I always keep my glasses on at all times whether at Disney, or Universal. I've done all the thrill rides. I am almost legally blind without them and on top of that I normally go to the parks alone. So, keeping them on is essential. While I've never lost anything in my pockets in the park, I feel a little worried about putting my glasses in my pockets due to worried about them breaking, or miraculously I do end up losing them that time I finally decide to store them away.
Only precaution I take is pressing my glasses to the side of my head at the end of roller coasters, as the sudden stop of the roller coaster and having the g-force speed disrupting is the only risk of losing your glasses in my opinion due to the force of the halt. Even then, it depends on the coaster as some do their stops more gracefully, but mainly it's sudden.
The only simulator I can even think of that would be violent enough to potentially take out glasses is Dinosaur and even then I did not lose them and I did not press them onto my face once during the ride, however I also would never go on that ride again, because of how painful it was for me.
Typically, if your glasses are correctly fitted, which they should be, they should remain on your face.
Also, hat's are easy -- Take them off.