Hi Lois,
Your pulse and tongue description tells us a lot. Deep pulses call for either aromatic or sweet flavoured formulas.
Given the wet and swollen nature of the tongue, we can conclude the dog is Damp, and can't handle that much 'sweetness'. You were wondering how much of that is due to steroids, but drugs should be considered to only aggravate the latent tendencies of an animal to begin with.
Viewed another way, regardless whether the pulse and tongue are steroid-induced or disease-induced, they tell us where the dog is at, and the way forward. If the deep pulse the steroids have 'created' hasn't solved the dog's problems, then we need to now do the opposite. Inflammation always must be viewed as a staged process, with the first goal being the limiting of damage and congestion; and the second later goal being the re-ordering of vasculature, repair of tissue, and removal of debris and inflammatory mediators. The former requires removal of the blood supply, the latter the return of the blood supply. Steroids and NSAIDs are great at phase I, but terrible at phase II. Herbs excel at phase II. Aromatic ones, especially for neuromuscular conditions, excel at this second stage or phase.
Given the above, Supple Spine (Du Huo Ji Sheng Tang) is probably too sweet or tonifying. I would start with San Ren Tang. In the last couple of years, we have found it works well for disc disease.
Another option might be Yi Yi Ren Tang, which is slightly more warming and tonifying. I'd start with one of those two.
Lastly, how does pred increase thirst? It is best viewed as not only cold but very tonifying. To an animal with latent Spleen problems, it's too much to handle, especially when it is also cold. Dampness is produced in response to this cold cloying nature.
Just as assuredly as Yang and Yin morph into each other, however, the excess Yin state induced by pred becomes an excess Yang state. While there is a low fire under the cooking pot and the animal is physiologically chilly, it becomes pathologically hot. The Damp slows the circulation of Blood and Qi, which in turn are driven by Heart Yang. This Yang is released as a sort of heat of friction. It is now a physiologically inactive, but no less 'hot' form, known as Damp Heat. Heat of any source raises the animal's thirst, and we go from having a chilly animal with digestive issues, for example, to a hot animal with Cushing's.
So, a long answer to your question. Hopefully it clarifies things for you and the advice is helpful.
Steve
Steve