The winlite fwts I have handled have had McMillan fwt profile stocks (Schnabel), pushfeed action, no cheekpiece, and no checkering. I believe they came with or without a floorplate and were made in the mid 80's.
I like them, a lot. Not sure they came in 7x57, but if I found one in a McMillan in 7x57 with a fwt barrel in decent shape, I wouldn't hesitate if the price was reasonable. At 560 in Canada I'd jump on it, fast.