First comment is on point. Get the JR Rail Pass. Take the Shinkansen bullet train to Hakodate or Nagano then rent a car to your local destination. I recommend going to both if you have time, but to be flexible so you can bullet train between the two. Hakuba Valley is where the Japanese Alps are which means the best terrain. Hokkaido is more quiet, in many ways. Snow should be plenty up there but it was less than legendary for us in Jan 2017.
I agree with hiring a guide, but how you do this all depends on your current experience, ability, and goals.
We (my wife is more badass than me) hired a guide for the first 2 of five days in Niseko and first 2 of 8 days in Hakuba and both were best decisions ever. We have lots of experience and were able to learn enough from our guides to learn entry and exit points, avoid major hazards, and be exactly where we wanted to be when it got deep.
And immerse yourself in culture. Raw fish, rice, and ramen; Triangle sushi at Lawson and 7-11; Samurai castle in Matsumoto; Onsens; Snow Monkeys.
https://www.newschoolers.com/videos/watch/868682/LovelyMoon-in-Japan---SHORT 
