I hunt that way a lot. I hunt family ground and have hunted them with bow, muzzleloader and rifle. Have seen a lot of failed attempts with a bow - you need cover to get close to them and there is not much around. Early season with a bow is your best bet because the crops will still be in. Once harvest is over, the deer head for the hills and big draws where your only cover is really yucca plants and utilizing terrain to your advantage. While you can sneak in CRP, good crp is hard to find and they're harder to find in it, let alone get within ~50 yards.
All things equal, your odds of successfully killing a good deer are limited out there because most of the good hunting is private, the good public spots are overhunted (trust me, we have wiha near us that is a laughing stock) and with a bow you have the odds stacked against you - the rut is also during rifle season. Your odds of success are quintupled with a rifle. I have bow hunted deer in CO several times and the deer hunting in the mountains is so much better in my opinion because good genetics and numbers aren't a factor of being on the right piece of private. From a time standpoint, you have at least a 5 hour drive to get into mules - that's far enough in my opinion that getting a little further west isn't that big of a deal.
All that said, I wouldn't wish to deter you - I love chasing them and it's an amazing part of the country. But from a time, money and success standpoint (if you're only hunting public land), there are certainly better places to go with archery tackle