Question
We have a huge cedar tree in our back yard that I would like to build a tree
house in using small 1 to 1 1/2 inch nails.  Will the nails make it likely the tree
will die?  Will the nails let in disease or pests?

Answer
The nails will not kill the tree. In most species of trees the nail hole could allow decay fungi to enter the tree and over time cause the tree to in the worst case become hollow. But cedar is not prone to decay so the nails will not really cause and problems. Now as the tree grows the nails will pull out or push the boards away from the tree. This will take several years to notice. I think you may need to use larger nails--1-1 1/12 inch nails if you use 1 inch boards will not go into the tree enough to hold the tree house. I would use at least 3 inch nails or larger if you use 2 x 4 s or bigger lumber for the bracing.
Rather than nails it maybe a good idea to use lag bolts use galvanized bolts for this they won't rust away on you.