Do you ever get this question? I get it all the time. Here's how I answer:

I live in the mid-Atlantic, USA. The best time to dig a tree is while it is dormant. The worst time to dig would be May when the tree has a lot of soft, rubbery growth. To dig a tree while it is actively growing is like a woman giving birth without an epidural (so I'm told).

For a variety of reasons, sometimes we dig in summer. The following quote is from a New Jersey field grower. At one time this nursery was the premier field grower nursery on the East Coast, sadly they are no longer in business.

Our nursery offers summer digging of certain plants that have proven successful with this digging process. This 'special digging process' involves slow-digging the tree, and irrigating it over the course of several days. The plant is then moved to a cool, irrigated barn where it is slowly acclimated. The charge for this procedure will be an additional 5% over the catalogue price to cover the additional labor involved in the process. Our nursery assumes no responsibility for the survival of this material.

Another scenario might be a landscape contractor who for reasons beyond his control must dig a tree in summer. Step one would be find someone who actually knows how to dig a rootball which sadly is a dying art. This should be done during the cool part of the day with the rootball full of moisture. If the tree must be transported THE WHOLE THING MUST BE COVERED WITH A TARP.

If you ever see someone transport (on the road) a leafed out tree that is uncovered you know that guy is a rookie and the foliage could be severely dehydrated. The tree is unloaded in the shade and put under a sprinkler during daylight hours. There it remains until it is hardened off.

Even with this special treatment some defoliation may well occur.

Some species are more easily dug than others. Finally a very important consideration, when was the last time the tree was dug? A tree that has only been in place for a year or two has a much better chance of survival than one which has been untouched for several years.

So there we have it, dig in summer if you must but let the client know, no guarantees.