Riding out on hacks over varied terrain is very, very different to riding in an arena. Hacking and lessons both have their pros and cons but I do personally believe that novice riders should do as much hacking as possible because it can teach you so much. Unfortunately riding school insurance often means this isn't possible, but there are always trekking centres if you want more saddle time outdoors. I learned to ride from scratch out hacking, never could afford lessons so I picked it up as I went along. Needless to say I had plenty of mishaps, scary moments and yes lots of falls - all part of the learning process
As a ride leader, when novice riders wanted to try / practice cantering I always tried to do it uphill so that I didn't need to worry about them being able to pull up at the end! The main downside to novices cantering uphill is that because of their lack of balance and/or ability to ride in forward seat they can pull back on the reins and use the horse's mouth to balance - so I always got them to stand in the stirrups leaning forwards and hold the mane, which (a) meant the horse's mouth got left alone and (b) made it almost impossible for them to lose a stirrup as they had all their weight on them!
As a ride leader, when novice riders wanted to try / practice cantering I always tried to do it uphill so that I didn't need to worry about them being able to pull up at the end! The main downside to novices cantering uphill is that because of their lack of balance and/or ability to ride in forward seat they can pull back on the reins and use the horse's mouth to balance - so I always got them to stand in the stirrups leaning forwards and hold the mane, which (a) meant the horse's mouth got left alone and (b) made it almost impossible for them to lose a stirrup as they had all their weight on them!