Does one "prune" a Purple Robe/Potato Plant?

They are tender plants and will have suffered in low temperatures - may even have died, sadly. They need 7 degrees to survive.

I had one which I cut back, took into my greenhouse for the winter, then brought it back out in the spring.

You were most likely asking too much for new solanums to pull through their first winter without help. They would have been far happier to spend their first winter or two in an unheated greenhouse or frame and giving them a couple of years to build up their roots and strength before planting out as I did with mine.

That said, any green stems produced last summer are very likely gone, but the woody parts might be OK - so be patient. Leave the old stems on then, if all's well they should start showing shoots in a couple of months when you can remove dead wood on stems above the highest shoot. Of course if you get no growth by May your plant has gone. But I wouldn't give up on solanums mine are older but I don't fear for them like some plants I could mention.