Whenever you get off your horse, for however long a period of time.. are you supposed to cross your stirrups? But why cross your stirrups when you could just roll them?
I cross them so they don't bang the horses sides....also there have been times I have got off sharp,and don't quite have time to slide them up the leathers!
Do you mean at places such as Badminton after the eventers jump off? This is so that they can loosen the girth/get the saddle off asap so that the horse can breath freely to cool off. Just think how you'd feel after running flat out over a couple of miles and a few big fences with a girth on, then you'll see why they do it - to be quick.
i do this in an emergency! gets them out the way quick, much quicker than rolling up, i have been known to pick right one up and cross over saddle as im dismounting and then flinging the left up as i touch the floor. Its just quicker! if i think of the times iv done they would include;
horse gone lame along main road need to get off and continue walking to somewhere safe to assess, cant stop to roll up stirrups because on a bend/theres bad traffic/horse wont stand still etc. and to leave dangling is dangerous and unfair to horse.
needing to dismount and take saddle off as quick as poss, because horse is badly injured/about to go down/caught up or something.
dismounting whilst out hacking, to go to some elses aid quickly, if they've come off their horse for example.
these are just examples that spring to mind immediately but i do it quite alot. basically for speed.