I had a walker mare who would pull this one on me, and someone gave me excellent advice. First, does she always spin in one direction? Yes, to the right in Satin's case. Is so, or even if not, as soon as you feel a spin comin on, tighten up on the rain opposite the direction of the spin. If she can't bend her head, she won't be spinning.
Laura "Not all who wander are lost." (jrr tolkien)