The time to prune black walnuts is when the sap is up in the tree, not coming up.  That's going to be at the end of May.  Walnuts do leak sap if you prune them earlier.  But usually sap lose is not fatal.  But it can attract lots of ants, wasps and bees, besides discoloring the bark with the leaking sap.  Do not prune in the fall or winter.  You do not want to injure a tree late in the season when it has no chance to heal. That damage could hurt the tree when there is a very cold winter.

Thank you very much.  Here's a follow up question.  Given that the weather is different each year, other than looking for the end of May, what do I look for in my Black Walnut to determine that the sap is up? 

If you pick the last week of May or the first week of June, it will work.  This year, the last two freezes killed all the existing walnut leaves in many parts of Michigan, so leaves are not a reliable indicator with our climate shift. By the middle to the end of May, leaves are emerging. 

The weeks will be easier to remember rather than leaf development.  Keep in mind that probably not much is going to happen if it is done the the third week in May.  Just don't expand it into June.  Hot weather is coming and the tree will not repair as rapidly...but walnuts are always slow.

Try to watch the tree's shape and prune when you only have a little to remove.  The best pruners rarely use anything bigger than hand pruners because they are watching where twigs and buds face and anticipate where the tree is going to grow.  It's like chess or checkers...you have to anticipate what is going to happen.  Good luck.

I can see the beginnings of leaves on the Walnuts, when other trees seem to be much further along.  I recall the Walnuts were some of the first to drop them last fall. 

As I briefly mentioned in my inital question these are large (tall) trees.  I'll definitely be using more than hand pruners, in this case.  My main agenda is to reduce the trees to a single trunk, each.  One tree only has two trunks, so I'll be done with it, this year.  The second tree has four or five trunks, so I'm thinking I should limit cutting to one per year.

I'm guessing these trees were planted by squirrels.

If you have a double trunk, the tree lost its leader when it was very small and now you have two competing leaders. The one with multiple leaders is the one that really needs to get fixed.

The comment about hand pruners is about keeping an eye on small trees. If you have other trees, just keep them to one leader when they are young. It's one thing to buy or inherit trees instead of growing them.  Good luck.