I don't normally backpack hunt during rifle seasons, but can offer some insight on weather, gear and clothing.
You should expect weather depending on where you are hunting. Photo is last year second season Colorado and is not unusual, but it can be colder with more or less snow or maybe really warm and dry. The slopes down or up hill are probably too steep for snow shoes. They might work hiking a trail, but I haven't seen anyone using them hunting big game in Colorado. They might be great if your vehicle breaks down or snowed in and you have to walk out.
Your question on boots and clothing is a personnel question, but on a backpack hunt pick wisely. As others have said snow totals can vary a lot from a couple inches to several feet in one storm. Shelter and sleeping bag are the two most important items to wait out storms. Tents collapsing during snow storms and being cold in an un-tested sleeping bag is no fun and dangerous. Four season tent.
I usually take three pair of boots in the truck then decide what are the conditions when I arrive. Uninsulated leather boots if it is dry and warm and expected to stay that way. Insulated leather boots if it is cold and dry and expected to stay that way. If snow is on the ground I wear mountain pac-boots and would carry extra liners and wear gaiters backpacking.
I would do similar with clothing and dress to the conditions when I arrive. My system is both top and bottom base layer, two mid layers, insulated layer (puffy coat and pants) and outer soft-shell, but I take rain gear if it is real wet snow. I wear either Kuiu or Sitka gear. Add light gloves, down mittens and F/O hat, F/O beanie and a cold weather F/O beanie for long sits and around camp or while sleeping.
Good luck and have fun
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