Howdy Quitestorm!!
I believe the film you're talking about is the 1954 film, Track Of The Cat with Robert Mitchum and Tab Hunter. It's about an older brother. who is a bully( Robert Mitchum). He's always putting down his younger brother( Tab Hunter) down, and their efforts to kill a marauding cougar. It's set during winter in deep snow. There is also a spaghetti western titled The Silence, which is set in the winter