I had to check mine before I responded, Mildot, but the one I have just has no kind of lining in the main compartment. It's just the one layer of lightweight nylon. I have an older version, so maybe the newer ones have some type of lining. It has the holder for water bottles on each side, and those are somewhat padded/insulated (plastic sports-type water bottles came with the bag). There is also a nifty little zipper compartment located underneath the water bottle holders, which is great for small stuff like hoof picks, spare latigo, or other things that are good to have but you may not need on every ride.
Now I feel really embarassed that I didn't explain very well what I was after.
You see, the SnugPax brand cantle bags have a fleece lining inside the sleeve (pocket) that fits over the cantle (not the side pockets where you put stuff in). I was wondering if the Stowaway brand is made the same way.
When my only saddle was a Wintec, it wouldn't have mattered. But I bought a new saddle at Equine Affaire and it is made of really nice calfskin. Now I know saddles are for using and the leather's going to show character marks, but I don't want abrasive nylon rubbing on a very visible surface all ride long.