I would say during rifle season, your best bet for a nice buck would be dropping down into a canyon where they is a clearing along a water source, and then sit there all week long. It is a low percentage game, but if you are patient you will eventually catch a decent buck coming to the water.
Chasing them around in the timber is more than likely going to be an exercise in frustration, that being said sitting by a water source might be too.
What you will find when you get there is that after you drop of the ridge you are in black timber, and spotting from any distance is difficult at best. You might have some success glassing the lower edges of a burn (hint: lots of the bighorns burned last year). these always tend to be game rich areas.
I would recommend ordering a forest service map and getting the "GPShuntmaps" files for google earth and going from there. My two nicest muleys came out of the northeastern corner of the Bighorns (they are both in my photo gallery if you want to see what I have been able to drag out of that area).
I have hunted the Bighorns for deer the past 2 years. Region Y the first year and R the second year. We did ok on both occasions but hunted our tails off. We get to Wy with 10 days to hunt and if we hunt a day or two in an area with no success we move on. We have pretty much covered both units north to south and the North is the better area if you want my opinion. Both regions are decent though and have good deer. Snow will determine alot though if you plan on hunting up north. We managed solid 4x4 deer both years with the largest in the high 60's but would count on finding alot of those. We strictly pack in on foot to get away from people and there are alot of hunters but once in a mile or so your pretty much all alone.
EDIT: Posted in wrong thread.
Thanks for the info.
I keep hearing about how the snow is going to play an intricate role in success or lack thereof. I'm from western PA and we keep our fingers crossed all the time during deer season that the snow comes.
Lay it on me guys....what do I need to know about how snow will affect the deer. How will it affect their behavior? What should I do if we have snow and what should I do if we dont?
The snow will have the greatest impact on the areas that you can get to, and a lot less impact on the deer. Once the snow hits the roads can get impassable quick. I have never seen the snow push deer out into the open country during the season, maybe some local folks can speak better to that. I think it was the 2009 season, and there was a decent amount of snow up on the mountain during the rifle season, and there were huge areas you couldn't get back into without a snowmobile.
Either way the deer are likely going to be holed up in the timber down in the drainages, and will most likely only break out into the sage once the season is over closer to the rut.
I have applied for Region R & plan on hunting the west side of the Bighorns ---However does anybody have any advise on whether it is better on the southern end down by the town of Ten Sleep (highway 16 ) or up on the northern end up by Montana? Also is there any accessable BLM land adjacent to the Bighorn National Forest? Any response / info is greatly appreciated -- Thanks