DuckDodgers, if the leather is good quality, but just dry, then you can re-oil it now that there's no water in the leather fibers and it will take the oil and soften up. However, if the leather isn't good quality, you may just be stuck with a stiff saddle.
Here's what I do when I get a new saddle. I put it on a 2x4 with the fenders soaking in warm water. When they are super saturated, I take the saddle and put it on a stand in the tack room and twist the stirrups 1.5 times around and put a section of board through the stirrups to keep them twisted until the leather dries
Then, once the leather has completely dried, I'll pull the board out and oil the heck out of the whole saddle with warm oil. After that, the stirrups are "turned" naturally and the entire leather is super supple so that you can twist it to whatever position is most comfortable for you.
If the rider has shorter legs, like me, sometimes they'll need to re-set their stirrups every few months.
Just as an example. This is what my saddle looked like right out of the box. The stirrups faced almost flat to the horse's side and the leathers were stiff so they put a lot of torque on my ankles and knees
Then, after a heavy oiling and a little bit of use, they still face a bit flat because I keep them so short, but they are supple enough that they don't inhibit my legs at all and I can turn my feet straight out to the side easily.
*old picture from right after I got it*
I do need to set them again though. It's been a couple of years.