Without seeing the problem first hand, I'm only guessing, but white, cottony masses on the woody parts of apple trees is often due to the presence of the Wooly Apple Aphid. These are tiny reddish insects that move slowly and are covered with a cottony material. Their populations are usually kept in check by a natural predator (tiny parasitic wasps), unless the wasps are killed by insecticides applied in the vicinity during the growing season. Woolly Apple Aphid colonies can be controlled during the dormant season with applications of horticultural oil. Be sure the oil is sprayed on both the upper and lower branch surfaces to smother the insects and their overwintering eggs. (If you were living in a wet, humid area, I'd guess the white, flakey stuff to be lichen or algae growth, which is easily controlled with a dormant season application of lime-sulfur.)
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