hello and congrats on drawing your first tag. All the previous advise is great. I haven't hunted NM but I would assume you might encounter some steep terrain so you will want to be confident you can make those type of shots. Hopefully your muzzleloader is scoped and you have worked up a good load/bullet combination for potentially long range shot. I would want the confidence to know I could shoot out to 200 yds for western hunting with a muzzleloader just incase mr. big steps out. Good luck on your hunt!
Oh yeah, another thing about practicing. The more you shoot the better your muzzle loader will perform, the reason is you season the barrel. Also make sure you have loads of cleaning supplies to take with you.
wow man there is so much that goes in to deer hunting but the best advice i know of has already been said talk to the experience around your specific hunting area talk to the guys at your local hunting and fishing shops alot of people who hunt also spend the summer fishing and other outdoor activities so if you can find a place like that and just strike up conversation alot of time you can grab good advice for your area from alot of people hunters usually are willing to help with there experiences ive never met a hunter thats not willing to sit and tell his own stories. take the good the bad and sort it out later. good luck and congrats on the draw.
Jesus Said "come with me and i will make you fishers of men" matt 4:19