I would build your walls using your standard 2x4, or 2x6 framing, starting in a corner and running your studs 16" on center, making sure that you have a nailing stud in the corners for your wall covering.
As far as the frost, it all depends on your location......If you would, put your location in your profile, so it's easier for us to answer questions like this......But as far as frost, there SHOULD be enough stone underneath to take care of any frost heave that may occur. Depending on where you are located, you may not even have to worry about frost.
And building a stud wall really isn't that expensive. Sure it's going to be more expensive than running a few horizontal girts, but I believe you would be more satisfied with the rigidity of a standard stud built wall. Plus you'll have an easier time insulating it.