Sorry for this generic answer but it is the truth.
When the snow gets deep enough to cover their feed up high to where they can''t get to it. It might start in October or December, it just depends on the year. I know of a herd in Utah that winters at 9500' + just because the wind blows the snow off of the high ridge that they live on and there is feed all winter long.
Like this last winter for example. Where I live here the winter was so mild I never saw any elk come down as usual. In general there are several hundred not far from the house by December/January but they never made it all this year.
Hunting can be slow and frustrating if Mother Nature throws a warm hunting season at you. But things can take a drastic turn for the better with the onset of a cold snap. Whether you get snow or just a good, prolonged cold front, the hunting can improve on a dime. But cold whether can also make certain parts of the hunt more tedious. Here are some things to keep in mind when your prayers for cold weather finally pay off.
You can see a your quarry's breath when it is cold outside...