I have moved a fairly large golden barberry in the heat of summer. It was quite traumatized but I kept it well watered and it survived. Less than a year later I moved it again and it did well. Moved another one about a month ago before it leafed out and it didn't skip a beat. I say go for it. My only concern might be the new soft foliage is too tender, but I have also had them re-leaf after being stressed.

I would say the best time is fall but if you keep them well watered it shouldn't be a problem to do it anytime.