7mm-08 will be fine. Especially if you are competent and comfortable with it.
As Barefoot said, unless you intend to be in an area where the shots are expected to be +400yds then a 7mmRM would be a good option, otherwise stick with what you have. Use the money you were going to spend on a rifle and get a decent pair of alpine boots, and good quality warm clothing. Make sure you have a decent pair of binoculars too.
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