I never knew this! Who said you can't teach an old dog new tricks? I have a bolt of Warm and White on my longarm and, as Jingle said, it looks the same on both sides. I went the website and found this in their FAQ:
Is there a right or a wrong side to Warm & Natural or Warm & White?
No, there is no right or wrong side of batting but there is a "scrim" side. When manufacturing Warm & Natural or Warm & White, the cotton fibers are layered onto a scrim - a thin substrate material. During the needle-punch process, barbed needles push the cotton fibers through and entangle them into the scrim. When quilting Warm & Natural or Warm & White, it is usually easier to do so in the same direction it was needle-punched - the cotton side facing towards your quilt top and the scrim side facing to your quilt backing. With Warm & Natural the cotton side is distinguished by its leaf & stem remnants (face to quilt top). With Warm & White there is a side that is shinier and smoother. This is the scrim side and should face to your quilt backing.
You have to have good light or younger eyes than mine to see the shine, but it's there.