Being a guided hunt, I am guessing you will not be 'killing yourself' hiking up and down a ton of miles with lots of elevation gain / loss, like a typical DIY hunt on N.F. But even a guided hunt is most likely going to involve a lot higher physical exertion level than any whitetail hunt. Good boots can't be stressed enough. There are lots of options on brands (Lowa, Kenetrek, Crispi, Hanwag, etc). Don't expect your whitetail hunting boots to work. Making sure your boots are well broken in and fit correctly will help keep you hunting. Blisters will end your hunt quickly. I like the Lowa Tibets and the Lowa Ticam II boots for hunting in aggressive mountain terrain. Both of these are uninsulated and have worked well down to 0 degree temps with deep snow. Quality merino wool socks are a wise choice too.
Your whitetail hunting clothes typically don't 'breath' well enough for high exertion / hiking. They can work, but they are not ideal for high exertion hiking. Getting soaked from sweat in late October by being bundled up too much can lead to a miserable situation. Mid wt merino wool base layers are what I use and they have worked well. If your budget allows, check out Kuiu, Sitka, First Lite. These are probably the most widely used brands that focus on western mountain hunting.
Physical Conditioning: This is usually the limiting factor for most of us when hunting in the Rockies. The only advise I can give is to be in the best physical condition that you can get in. The altitude is something that you can't prepare for, but you can help yourself by showing up in good physical condition. Your guide / outfitter will most likely work harder for you if you are able to 'get after it' day after day.
The Hunt Backcountry Podcast / website has some good resources to help educate you on the various aspect of western hunting. These guys focus primarily on elk hunting, but a lot of it applies to mule deer.
Good Luck on your hunt.