There's a good neighbor policy that landowners generally follow (see campbell timberland hunting lease agreements available on the web). Landowners livestock are just as likely to cross a fence as is a hunter's dog. If a dog harasses livestock, or if the property owner feels threatened, then the landowner may be able to shoot your dog.
I worry about this all the time. I hunt all over the state.
http://www.roaddrivers.org/fivedogskilled.htmhttp://www.denverpost.com/ci_8691905?source=pkg