Many people want to use natural woods for their small animals to chew on. When going out and pruning trees there are a few things you need to be careful of. First make sure that the trees are un-sprayed and free from any disease and or pesticides.
Next.. read over the list of safe and unsafe trees. This way you can be sure to pick the correct tree to cut. Finally after cutting the wood the next step is to process it. This involves washing (scrubbing with a good dish brush .. remember NO dish soap) then bake the wood in the oven at 250 degrees for about an hour and a half(this also depends on the size sticks that you are baking.. larger sticks = more time smaller sticks = less time).
When your done with that let everything cool and you have prepared a treat that your animal will love! 
Toxic Wood list:
Ginkgo
Sumac
Fresh pine
Fresh pinecones (sap needs to be removed)
Safe Wood List:
magnolia
Pecan
Mullberry