Just did two of mine. Threw them in our front load washer, used Woolite, gentle cycle with cold water. Hung to dry in basement. Came out great, with no damage to the embroidery on the fronts or the padded tops.
I have washed Clothes Horse covers! (Tee hee hee). All the instructions above are fabulous. Machine wash, gentle cycle, hang to dry (preferably out of direct sunlight just to be safe). They do dry faster and avoid fading if turned inside out.
Newer covers are made from different fabric that does not fade.