I always wear my glasses on all the rides, without a strap or concern. However my children prefer to take them off on all of the fast rides, including Splash Mountain.
I think it comes down to how comfortable you feel, I know I would not enjoy the rides if I were worried about my glasses falling off. But I have been wearing glasses for more than 40 years and have a good feel for what it takes for them to fall off. I also take care of my glasses (unlike my kids) and know they have a snug fit, so I don't worry about them falling off.
Personally, if you have any concerns get a strap or take them off, otherwise you will not enjoy the ride fully. And don't we all go to DLR to enjoy the rides?
On a similar note, does anyone else enjoy counting the hats on the Matterhorn tracks?