Old post but I thought I would answer.
Headed back for my 10th cow hunt in November.
Now you have to use a guide. This started a few years ago. My previous groups went 9 for 9 in our hunts. If you can get Cloyce as your guide it would be great. He's a full blooded Apache and has horses to get your elk out if needed. He knows the res.
Put in for at least two of the three hunts and fill the application with all four spots. Anything less than 4 people and your chances drop.
Tons of elk and you will see some bruiser bulls.
It's a beautiful place and a big place. Killed a lot of in Turkey Canyon and Eagles Roost. Last hunt I shot out the first morning hunting the tree line where the flats meet the hills. Can't remember the pasture off hand.
It's a fun hunt. If your drawn early get a AirBnB, it's a lot cheaper. Be prepared to shoot anywhere from 40 yards to 6-700 yards. You never know.
You can call the Inn of the Mountain Gods hunting lodge in early March and ask about the application if it is not online yet. $25 app fee per person. Cow hunt is $740. Used to be $500.