Yes, they love cedar; no, the browsing shouldn't kill the trees. However, it does change the way they look, forcing the branching to be higher on the plants than normal. If you can deal with the odd look, you'll be okay. Might I suggest spraying the plants with a deer repellent? Newer ones last up to 6 weeks, so you wouldn't have to reapply that often. Mostly in winter when deer are hungry.