Shooting equipment
Bring a rifle you can shoot well and be prepared to take shots in the 300 to 400 years range. In the Northeast I use my 30-06 most of the time. It is a very versatile gun with a large selection of bullets but I do not like the 30-06 caliber past 300 yards. I prefer the 270 or the 7mm mag. Again be comfortable with your rifle. Hunt with it and practice before your trip. Put a nice sling on your rifle. Make sure you use a wide and non-slip one.
Understand the ballistic characteristics of your ammos. The trajectory of your bullets will be very different at 6000' elevation with a freezing temperature from what it is at sea level when the temperature is in the 50's. You can use one of those on-line ballistic programs to help you understand the differences. Print few ballistic charts for your hunting conditions for different altitude / temperature conditions. You probably need the charts for 100 to 400 yards range.
Always carry a small field cleaning kit suitable for your rifle. Again make sure you know how to use it. You won't be able to play the CD and read the instructions after you dropped your rifle in the snow. Make sure your rifle is in perfect condition. Check all the screws are tight.
A box of ammos will be plenty. You do not need to carry more than 5 or 6 for a day in the field.
If you like you can bring your shooting sticks. They work well but they also add a little bit of weight. If you are flexible enough and can go into prone position, you are better off using your backpack as a rest. Do not mount a bipod on your rifle. Those things will hurt you when you carry the rifle on your shoulder.
Optics
This is really important. You are going to use your binocular for several hours a day. Make sure they fit you well and you have proper eye relief if you wear glasses. You can use 8x or 10x binoculars. 10x binoculars will require some sort of support. I like the 8x better.
A 3-9 or 4-12 scope will work best. Make sure your scope works well and you know how to use it. I posted some scope drills in the Resource/Download target area. You will need to adjust the elevation and possibly windage on your scope. If you do not want to adjust the elevation and windage on your scope make sure you know how to use the reticles at different magnification. Do not rely on the old Kentucky windage to correct for wind and distance. Zero your scope at 200 yards before you leave. It is also OK to zero your scope at the maximum point blank range but make sure the ballistic tables you bring match your current setting.
Bring also a good range finder. If you hunt whitetail deers in the Northeast you won't be able to figure out the distance in the empty space of the West. Get a range finder that works up to 600 yards and if you can get one that gives you the angle above and below the horizon as well as the horizontal distance. If you have to shoot upward or downward you will need the horizontal distance to figure out your elevation.
I never bring a spotting scope to go hunting. I think it is just too much equipment to carry. I do not think you will need it if you have good binoculars.
Make sure you have good sun glasses with UV filter and polarizing lenses. The reflexion of the sun on fresh snow can blind you.
Others
I always bring two knives with me plus a small saw and/or a thick blade knife to quarter the animal if needed. One is a Swiss army knife. It has a small toothpick and a small tweezer that I can use for minor medical emergencies. It is also my lunch knife and I always keep it clean. I also carry an Alaskan Guide Buck knife and a pair of disposable vinyl gloves to gut the animal. You will also need a small sharpening stone.
I bring along a light emergency kit. You do not need to bring anything too fancy but you should be able to take care of small problems such as a cuts and scratches.
Make sure you carry a topo map with a GPS or compass. Remember that a GPS with a dead battery is nothing more than dead weight. You will also need a small flash light. The newer flashlights have LED instead of incandescent light bulbs. LEDs provide more light and use less power. They are also more durable. Some of the newer flashlights do not have battery. You turn a crank to charge a battery to give you few minutes of light. This is a nice system.
Bring a good backpack that is comfortable to carry and has an hydration bladder in it. Make sure you put in your bag your signed licenses (if it is not signed you are likely illegal) and your tags. You will need some toilette paper, a space blanket, water proof matches or a fireflint, your food for the day, and a rope.
You will also need appropriate clothing for the expected conditions and possibly some hunter orange. Many outdoor stores have training classes that will teach you how to layer your clothes and what material to use. The newer fiber are really nice, but again wear them when hunting at home before you fly on your dream hunt.
I hope this article will be helpful. As usual be safe and use common sense. Talk to local outfitters and guides, check the regulation on the state web sites, get a proper weather forecast, and let people know where you are going.
Happy hunting.