Although most children's paint claims to be washable, we haven't always found that to be true. So to help out, we don't bother pre-treating or soaking, instead, we turn to our ever trusty bottle of dishsoap!
Before putting the bowls/tubs/containers of paint on the table, we add a few drops of soap (3 drops to 1/4 cup paint). We've used everything from Dawn and Palmolive, to more eco friendly choices without any difference in results.
Since we've started using soap in our paint, we haven't had a single stain we couldn't get out. The soap doesn't allow the paint grip hold of the fibers in the fabric in the same manner and washes out, even with cold water.
(Please check labels on upholstery before cleaning with water.)