Old Snow theme works with 1.6.2 but there are few things you should know.
1 Top bar Login form: Since 1.6+ has improved login, it will take user to the login page after submiting topbar login form instead of getting logged in
2. User profile page layout: This is not going to affect functionally but only visually
4. Some visual changes like color, buttons, sidebar widget, background etc.
So functionally the topbar login there is no such functionally issue.