Please excuse the slow and awkward saddling as I am pregnant and getting a saddle rubbing on each side and working my way up with it is difficult for me at the moment. I like to let them see and feel it on both sides comfortably until it is on and give myself enough time to get cinches tight. I try to keep my lead rope tight enough if they try and walk off I can stop them until saddle is tight, but with proper groundwork they should just stand still. I replicate the motion of “throwing” a saddle on with my rope to prepare for this but usually “set” it on nice and gentle for their first time.
Everything about the saddle, except for the saddle itself is prepped in our groundwork. We have them mentally accepting and calm with seeing something whether a flag or rope on both sides at standstill, w/t/l and with head flexed. They can change sides with previous examples quickly without panic. They work on “cinching” motion and pressure with a rope, as well as pick up all four feet. They can move their hips, shoulders and keep softness and responsiveness in those actions with a soft head and calm but responsive mindset. Sometimes no matter the preparation, they feeling of an actual saddle in motion with weight, sound etc can still be a new feeling to get used to and horses will still buck, but that is no indicator that anything but the first experience of it, will ever occur again. I prefer them to never learn to buck at all.
After this we worked out the same concepts atop a saddle horse and let them get used to me moving with them/above them while I let them see my rope or hands on their off sides, and shake the saddle around with the horn too add pressure and weight. I drove him as well and he did great with the preparation for that in groundwork as well. This horses first ride was uneventful and great the next day.