When fully dormant, that would be the ideal time. But it does not mean do not transplant the rest of the year. Summer, because of low humidity, drying winds and high temperatures, is the worst time but it can still be done if you devote time and provide some TLC after transplanting. Some people, when attached to the shrub for sentimental reasons, will propagate it before trying to transplant it.

Shrubs that start leafing out are breaking out of dormancy. I have some just starting to wake up. The leaves are still tiny (

I'm planning on transplanting several 3-4' tall mopheads this weekend as well. in Zone 6 mine are still in dormancy, I'm guessing--the only leaves they have on them are dried out ones from last year. The buds on the stems are swelling but still very tight and small.
Hopefully we both have good luck!!