The singer and her actor lover - who have been dating since they met on the set of their TV movie 'Northern Lights' last year when they were both married to other people - have denied reports their relationship is in trouble and are enjoying a romantic mini-break in the mountainous state.
LeAnn took to her twitter account to post an image of the pair puckering up for the camera, with the title "Kisses!", and revealed plans to lock Eddie away in her cabin for a few hours.
She tweeted: "Going to lock myself up in my cabin with Eddie Cibrian, if you know what I mean. Nice dinner, amazing food. God, what a beautiful day!"
The couple - who recently revealed plans to move in together - showed off their romance after claims Eddie has been cheating on LeAnn with his soon-to-be ex-wife Brandi Glanville, who he has two young sons with.
He also took to his twitter account to deny these claims and blame his estranged spouse - who he is currently divorcing - for the story.
He wrote: "Once again my ex has stooped to a new low attempting to sabotage my beautiful relationship with LeAnn. Not surprisingly the only magazine that decided to run the story shares the same credibility and delusion as my ex. They should be ashamed of themselves."
However, LeAnn doesn't seem upset by the reports and is fully supporting Eddie.
She tweeted: "Montana is the most peaceful and beautiful place I could be w/ @eddiecibrian right now. We have NO service other than the main lodge where we are staying, so we are escaping. I thank you ALL for your love and support. I know more than anything in this world that @eddiecibrian loves and respects me more than anything in this world. Nothing and no one will ever change that. Montana is magical! Peace it brings! (sic)"
LeAnn's seven-year marriage to Dean Sheremet legally ended in June this year, after she embarked on an affair with Eddie in early 2009.