Not a fungus. Instead, woolly apple aphids.

To be certain that's correct, squish some of the woolly stuff. If it's the woolly apple aphid, you'll see a purple stain.

If so, they're specific to apples. The bad news is that they are also on the reoots.

Even so, my several apple trees with these aphids were still productive when I moved and the trees were about 15 to 20 years old.

Yes, that's exactly what it is! Thanks a lot - I saw white fluffy stuff around trunk wounds and assumed fungus.
*wipes purple goo off fingers*