Typically "wool applique" refers to felted wool. I use either pearl cotton or 2 strands of embroidery floss (I like Aurifloss) with a button hole stitch -- or some decorative stitches. Also, I've found that Heat n Bond is the best fusible web for wool applique.
Felted wool can be washed, but I definitely don't plan on washing them as often as cotton quilts. I've also been taught that if you're using wool/felted wool to make a bed quilt, you want to either back them in cotton and turn the cotton edge over a bit so that it's the cotton against your chin rather than the wool to protect the wool ... or you could make some kind of protective sleeve out of cotton. Personally, I prefer to keep wool applique for table toppers, wall hangings, etc so washing once every 4-6 months by hand is sufficient.