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.
First make sure your gun is safe, remove the bolt and clean your barrel from the chamber to the end of muzzle. Clean the barrel using butchers bore shine until a patch comes out white. Run a total of 5 separate patches soaked with denatured alcohol through the bore and let dry for 30 minutes. Insert a cleaning rod with a jag and a dry patch into the neck of the chamber. Make sure it will stay there through the next process. Now using another cleaning rod, install a patch that has been coated...