We are doing the same kind of riding that thenrie is talking about. My boyfriend, who´s a big guy, uses the Stowaway set that Phantomhorse has in her photo. He gets in a water bottle, spare socks and t-shirt, snack, a waterproof, and ID.
I use these ones : ORTLIEB Produkt-Details
Took a long time to find but they are working out very well. They sit over the saddle blanket so no rubbing. I changed the attachments from an ´X´of straps just behind the saddle to four small straps with clips that attach directly to the rings behind the cantle. There is a belly strap which virtually stops all flapping - if kept properly adjusted it´s no more cumbersome when moving through brush than the second cincha on a roping saddle. My mare, who is not the most level-headed at all times, doesn´t have any problem if she brushes the pack against a tree and it pulls against her belly. It´s attached by a clip to a ring on her girth.
I carry a human and equine first aid kit, waterproof, our papers, our lunch for the day, my diary, the map when we´re not needing it, water bottle, and even a small computer.
Quick photo of them on the horse, the first time out (the slack that you can see in the belly straps is now gone, since I adjusted it and sewed up the loose part) :