[Cynical25]

My wide, short-backed QH does well in a butterfly-cut reining saddle with a 28" skirt (mine's a Continental Reiner C68 Xtreme Performer model.) I use a 5 Star butterfly-cut saddle pad in 30" length so it doesn't rub on my horse's loin like the more typical 32" length pads.

 

[lilruffian]

You can get saddles with rounded skirts. Many barrel racing saddles have them and work great on short backed horses.
But it all depends how much you want to pay. If you have a difficult horse then you may have to spend more to accommodate her but my first step would be to get her measured and send those into a reputable saddle maker if only to figure out exactly what sort of tree to get as sometimes our guessing isn't accurate. And luckily that part is free!
For example, I thought my mare (14hh with a short back and no withers) would need a wide tree saddle at best and was going to go ahead and order. Thankfully I decided to measure her up to be on the safe side and the results came back from Tucker that she needed an extra-wide. Still in doubt, I was able to borrow a wide tree from my local tack shop and sure enough, it was still too narrow.
A slight fit issue can be fixed with shims or a good pad, but you will need to either get a good saddle fitter out or run some tests yourself (going for a long/hot ride that will produce some sweat so that you can see which areas aren't making full contact with the saddle) to find out where the shims should be and what pad/changes might help.

 

[Smilie]

There are western saddles with Arabian trees, which are shorter


Arabian Saddles