I was there in May, and while I only visited Lower Antelope slot canyon (of the two Antelope slots), they most definitely WILL ask you if you intend to use the images for commercial use (print sales, gallery sales, etc), and if so, they will ask you for your permit, which you will need to have taken care before you visit. While I was there I saw one person who had not been prepared have to get out of line, get on the cell, and try to arrange something. I do not know if that person was ever successful. The advice I've heard is to take care of the permit several weeks prior to your visit.
In my case, I was shooting for personal use only, so I didn't have to go through the routine.
Horsehoe Bend, to my knowledge, doesn't require a permit.
-m