Haven't been there in a few years, but it will likely be winding roads. The elevation of Cedar Breaks is at 10,000 feet. No real way to climb that elevation without switchbacks. Can't specifically remember about drop offs though. Hopefully someone that has been there recently can help.
The 6 mile scenic road IN Cedar Breaks is fairly level and an easy road to drive. It is the getting there that will be a little iffy. Both the road from Cedar City (hwy 14) and the road from Parowan (Hwy 143) go up canyons with winding curves. I personally do not consider either one as bad. Probably the one from Parowan would have less steep sides. You can also get to it from the East side from Hwy 89.
Just know that you won't be able to get away from mountain roads anywhere in Utah. But the paved roads are all safe and well traveled.
We do this drive several times a year, you should have no problems no matter which way you go. If you take HWY 14 out of Cedar City it's a little more "twisty" but a beautiful drive. The road through Cedar Breaks is very easy, just gentle curves, no drop offs. The road to Panguitch is an easy drive, no twists, no drop offs.
That's our favorite area for Summer fun, hope you enjoy the different views and lower temperatures!
Thank you so much everyone....