I use Pellon 360 Tear-Away Paper Stabilizer for satin stitching. I get it at JAF. Full price is $2.99/yard but I always use a 50% off coupon or buy it when it's on sale for 1/2 price. The other option is a water soluble stabilizer like Sulky Solvy.
If you're thinking you want to try Freezer Paper, I would definitely try it on a scrap piece first. I've never heard of using it as stabilizer. Freezer Paper is used for turned edge applique when you're pressing the edges.