The spread of the Arnica fire, now mapped at 9,300 acres, has slowed over the last two days. The map below which depicts heat detected by satellites, shows a major reduction in heat compared to what the fire was doing two to three days ago.

An updated map of the Arinica fire in Yellowstone northeast of West Thumb, showing heat detected by satellites at 3:30 a.m. MT Sept. 29. The red areas contain heat that was detected within the previous 12 hours. The map also shows the Butte fire southwest of Cooke City which had quite a bit of heat Monday night. Park spokesperson Stacy Vallie told us that as far as they know it is not spreading very much and was last mapped at 180 acres. GEOMAC
But it certainly is not out yet. The Mt. Washburn web cam occasionally is socked in by smoke as the wind sometimes blows the smoke directly at the lookout.
Fire personnel have been running an irrigation system to protect structures. Night time temperatures have obviously been below freezing.

NPS photo

NPS photo
The weather today could be conducive to additional fire spread, with the forecast calling for 18 mph SE winds gusting to 28, a high of about 60, and a minimum humidity of 21%.
But rain is expected to begin by 6 p.m. this evening and should change to snow by midnight. A total of about 6 inches of snow is predicted through Thursday morning, which most likely will be the fire season ending event for Yellowstone. The forecast calls for chances of more snow all the the way through Monday, October 5.
(UPDATE at 7:38 p.m., Sept. 29. The Weather Service has changed the forecast. The rain has been scrubbed, and the snow is expected to begin Tuesday night at midnight. It should continue through Wednesday night, with about 6 inches accumulating. There will be a chance of additional snow every day through at least Monday.)
The biggest problem facing firefighters now is how to avoid having to deal with frozen and broken irrigation pipes and pumps as the temperature dips into the teens Wednesday and Thursday nights. Removing a massive irrigation system in the snow is something I imagine they are not looking forward to.

HERE is a link to a more detailed version of the map above.