I have used huge amounts of freezer paper in my lazer printers over the years with no problems. Freezer paper is what I prefer to use for the fancier paper piecing, because I can iron it into place and have it stay there. I also use it to back treated fabric when I want to print directly on cloth.
(BTW, I have had several printers since I started quilting, all HP, because my DH is always determined to get me the "next" thing, whether I want and need it or not. My current printer, however, is because VISTA would not recognize my older printer. My delightful neighbors and the senior center use my old ones.)