Can I put a clothes line or dog run on my tree?

Yes, but install it properly, so it will not do long term damage.  Every year we do post-mortems on trees that died because someone put a dog leash around the base or a clothes line around the trunk or a mechanical support for the tree around a large branch.  Trees are living organisms that are ALWAYS growing.  The living tissue of a tree is a very delicate thin layer located just beneath the bark so an encircling wire, rope, twine or cable will have devastating results if left on more than one year.  Use screw eyes or lags to install these things on your trees, even though it feels more harmful, it really is not. (ref: Cabling and Bracing Abstract)