I am certainly no expert on this, but I did watch the rams in a local herd for a few winters.
Any rutting activity with any animal takes lots of energy and fat reserves, often leading into the worst weather of the year. They need some time to forage and get healthy again, so I am sure they do what they can to eat before the grass is totally covered with snow.
I have also been told that sheep from one herd often rut at much earlier or later times than another herd that is not that far away. So when the rut ends, is sometimes hard to tell.
At any rate, the local sheep I watched hung with the ewes until it appeared that they were all bread and then they seemed to join their buddies again in a ram band. We watched 5 rams in a band for most of the winter. Sometimes we would again see them around ewes, but it was obvious there was no rutting going on.
I also imagine that it depends on how much territory they are covering. These sheep (ewes and rams) seem to hang out in pretty much the same wintering area.