You may find these questions for group discussion helpful, from our "quicknotes" pages on the novel here at eNotes. The link appears below.
We have also just recently added a full analysis of Frazer's novel, in which you will find summaries, character analysis, themes, style, historical content and more! The link to these pages also is below.
There are several teacher-based sites online which offer free lesson plans with study questions and essay topics for novels. Do a web search for "lesson plans, cold mountain" and see what turns up. Two of my favorites are the Discovery Channel and History Channel--since this novel was written about the Civil War, you might have some luck there.
I might be a little late with this, as I see the question is from November. Perhaps for next year, get the curriculum unit on Cold Mountain produced by The Center for Learning. No, I am not affiliated with them, just a teacher who uses their products and they're mostly good. Spark notes has a decent study guide and quiz too. I often take the Odyssey angle and have students compare/contrast the events/allusions to the Homer's Odyssey. Many get in to that because it's something most have read earlier. Good luck