A general rule of thumb for trees sealing after wounding is to cut when they are actively growing, hence the recommendation for earlier in the year pruning.
Kate is correct on trees will sprout less if pruned in the summer as most of their vigorous growth has been put on in the spring and they are slowing down. So this is what we recommend when people want to minimize grow back.
Deadwood or removing weak limbs...any time, and again I agree with Kate in that it is far easier to see when there are leaves on the trees. Which translates to faster work, and generally cheaper for the client.
We always tell people there are 3 kinds of trees, angiosperms, gymnosperms....and fruit trees. In our books, they are kind of out there on their own. We generally prune them in Jan/Feb but you can prune them any time....depending on your goal.
I would be reticent to do a harsh reduction in the heat of the summer. You also need to be aware of any diseases that may be transmittable during the growing season that would be less problematical in the dormant season.
Another side note on working on apple trees during the growing season.
They are a hellacious mess to clean up!!! We have ended up with a chipper completedly clogged with apple mash. And you have to be careful where you dump the chips because every critter in the neighborhood is going to be there munching away. Probably not so bad unless you live in bear country...so for us, not so good.
Posting pictures would allow us to help more specifically.
Sylvia