
| Iorthol | 
 
	
 
                
                
              
            
            If you want to get into technicals, it means that you have a -4 to hit and AC until you spend an AoO provoking move action to remove the status. 
Being on the ground could mean, on the floor, on the back of your horse, whathave you, but being on a horse does not make you immune to the prone status. It's up to the DM to decide where the ground is in regard to your toon.

| Pirate | 
 
	
 
                
                
              
            
            Yar!
This situation doesn't only apply to firing a culverin, but also for failed trip attempts while mounted (say by a Cavalier with the Mighty Charge 11th level ability, or anyone mounted and attempting and failing to trip an opponent without a trip weapon), getting tripped, etc.
Personally, I would go with it knocking you "prone" but still on your mount/in your saddle, then follow it by a Ride check to stay in the saddle. Failing that check means you fall off your mount, while succeeding the Ride check means you stay on your mount and in your saddle but are knocked back/prone/splayed backwards/hanging off the saddle awkwardly and would still require a move action to right yourself (and each round you don't try to right yourself you must continue to make ride checks to avoid falling off due to being prone on your mount, aka not riding in the saddle properly).
EDIT: kinda like THIS, or THIS, or THIS, or what's happening to the guy on the right, or THIS GUY, or in many clips of jousting and the like where the guy gets hit, collapses backwards in the saddle, and after a few seconds either falls completely off or manages to recover, but definitely NOT THIS!
^_^
~P

| Doomed Hero | 
 
	
 
                
                
              
            
            You can definitely "go prone" while riding. Think of any western movie where the rider ducks low on their mount, or leans off to one side to use the horse as cover (a good tactic if you have Mounted Combat and can use a Ride check as your horse's defense)
That being said, both going prone and recovering from prone while riding should require checks. Those aren't easy maneuvers to pull off.
What you really want to do to someone who is mounted is Drag, Reposition or Bull Rush them.

| Iorthol | 
 
	
 
                
                
              
            
            "Stay in Saddle: You can react instantly to try to avoid falling when your mount rears or bolts unexpectedly or when you take damage. This usage does not take an action." It's not an exact wording fit, but there isn't a lot of difference between a horse bucking forward and a powerful gun bucking you backward. This is a DC 5 check.
I still say, if a feature says you are knocked prone without giving a save or resistance, then you're knocked prone, which means falling from a horse.
Why don't you just build a gun mount into your horse's barding?

| KA-BOOM! | 
 
	
 
                
                
              
            
            I'd rule: "Make a ride check or knock yourself out of the saddle. If you fail by 5 or more, you get dragged in the stirrup. If you succeed, your grip on the saddle and your feet in the stirrups kept you up. I DO hope your mount is accustomed to firearms...?"
covered under combat training... at least when I train them it does.
 
	
 
     
     
     
 
                
                 
	
  
	
 