Question
Is it OK to prune trees as long as it isn't between May 1 thru August 1

Answer
The pruning of birch trees should be avoided unless absolutely necessary.  Pruning of birch trees in spring causes high sap flow, attractive to migrating beetles.  In an area with high incidence of bronze birch borer, avoid pruning.  If necessary, prune in the fall during the tree's dormancy period.

Dead limbs can be cut at any time of the year. Do not cut it back flush with the trunk but you should see a small swelling near the trunk this is the branch collar cut to this. On large limbs it is better to make a couple of cut cut about a foot or so up the branch and this will keep the branch from splitting and removing bark from the trunk. make the first cut underneath and the second about an inch up the branch leaving a foot of branch stub. This branch stub then can be cut without the weight of the limb splitting the bark.