Hi Vanessa,
Welcome!

Just personal experience, but ice is intolerable for me. My RSD started in the cast (but I didn't realize that till later) after a colles fracture with complications. The day after the cast came off I was sent to PT. Up till then, it had been extremely painful, with pain the first and foremost symptom.

After the PT, they iced my arm in polar thermafrost, it seemed, for 20 mins. It was the worst agony of my life, bar nerve tooth pain, but they wouldn't remove it, sat and watched me right the way through as I suffered what seemed like having my arm plunged into boiling water and kept there.

When the ice was removed the arm and hand looked like it had been severely burned, was dayglo bright red, suffused in nerve pain but fizzed and hummed like a sound and that was it, RSD proper. It was like the ice was the gelatine that set the RSD jello.

So, while I believe desensitization is necessary for many reasons, and I give myself a "refresher course" every so often, I do it without the aid(!!) of ice - there is no situation in life that would induce me to go near ice, under any circumstances. I know "in my bones" that icing it would bring the RSD back up to the 10 in terms of pain, and get the condition roaring back full blast.

My arm and hand, especially, is very sensitive to cold, I've cut the arms off old sweaters and put those on the arm and wear double gloves, very loose-style, in the cold. So for me ice is completely out of the question.

We're all different, though. As far as the PT went, I found contrast cool and warm water immersion to be the most helpful. Hope this helps...
all the best