Have not been to Aomori springs, sorry.

December is a poor month where you are at the mercy of snow cover more than anything. Look at the 2015 and 2016 Dec figures for Hakuba and you'll see even past Christmas they were sometimes skiing on rock and grass! Hokkaido is the only place for Dec skiing if you need to book in advance, and they charge like wounded bulls at that time.

i agree late feb is preferable, though weather is as likely to shut things down at either time I feel. Late feb has possibility of rain which solidifies and makes the runs bulletproof. No one wants to fall on sheet ice.

I do truly believe that the backcountry is much more accessible in Japan than anywhere. It's harder on skis so you'd want powder skiing experience from the resort, but I know 2 guides (one is a local, Japanese lady) who would be excellent for beginners if interested.
This year the big snow trip for me is Kyrgyzstan but I will be in Niseko region late Feb, too.