The following is directly from the Warm Company's website. In other words, scrim side goes down.
No, there is not a right or wrong side but there is a “scrim” side. When manufacturing Warm & Natural or Warm & White, the cotton fibers are layered onto a scrim – a thin nonwoven substrate material. During the needle-punch process, barbed needles force the cotton fibers through and entangle them to the scrim. This is what holds the batting together without glues allowing quilting or ties to be up to 10″ apart. 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 toward 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.