If you dropped out several places and made your travel route linear, you could make a 12 day trip, starting in Sapporo and then heading one-way south.
• Sapporo - base for 3 nights
• Otaru - day trip from Sapporo
• Niseko - Drop unless you want to ski. There are several towns through this area that give access to ski slopes.
• Lake Toya & Noboribetsu - One or the other but not both. Toya has Showa Shinzan and the cable car to the volcano and hot springs. I'm not sure if the tourist boat around the lake runs in the winter. Noboribetsu has some nice onsen ryokan that would be good for a night or two but overall it's a tourist mecca with huge concrete onsen hotels. To give you an idea, the lower town closest to the train station comes complete with a marine park and a bear park and even an "Edo Wonderland" (Date Historic Village) theme park.
All of these areas take time to travel through as the distances are far and there are no shinkansen until you get to Shin-Hakodate. Even then, the shinkansen doesn't get you to many of the places you want to go, so you have to change to slower trains or buses. The places you have listed aren't "hidden gems" and you would need to drive to get to out of the way onsen or small villages.
• Asahikawa - drop as it's in the wrong direction (north of Sapporo).
• Hakodate - one or two nights. The asaichi is good for seafood and the views from Hakodate-san at night are great. The bus to the top doesn't run from November to April so you have to take the ropeway (cable car). It will be cold at the top. I usually stop for multiple days here as it's a nice small city.
• (would love to visit Furano but I don't think it's really a winter spot?) - drop
• (would love to visit Abashiri but it's so far, even from Asahikawa) - drop
And here are the spots in Tohoku:
• Aomori & Hirosaki - Unless there's something specific you've heard about these places, you could probably drop both in the winter. Hirosaki is famous for its apples and the castle park is mainly notable for having a castle in an area where there aren't many. I've wandered all around Aomori and taken the ferry from and to the city, but haven't found too much of interest when the matsuri isn't being held.
• Lake Tazawa & Nyuto Onsen - There's a JR bus direct from Aomori to Lake Towada instead of Lake Tazawa. Either for 2 nights. Towada-ko has the Oirase Gorge on the north side of the lake. Tazawa has Kakunodate south of the lake where there are some areas with old architecture from the Edo Period.
• Akita - drop - I have a favorite izakaya here but that's mainly why I go here now. The castle is gone replaced by a park and shrine, and the lantern festival is in August.
• Yamagata - drop - if this is a must stop, at least it's winter. It's hotter than h in the summer.
• Sendai & Matsushima - Matsushima only - 1 night.
• Fukushima - too many places with this name - city and prefecture. I've spent a total of 1 month in the prefecture and enjoyed the sake distilleries around Kitakata north of Aizu-Wakamatsu and the post town of Ouchijuku the most. There are ski areas up around Bandai-san.
The trouble with your outdoor activities in winter is that where you want to hike will be in deep snow. That leaves snowshoeing and skiing. If you want to try skiing, somewhere around Niseko and Hirafu/Kutchan would get you close to a good beginner area. The snow monsters are at Mt Hakkoda south of Aomori, but you need to hire a guide. An English woman skier got lost from the top of the ropeway to the base a few years back and had to spend the night on the mountain.
http://aomori.showcase.japantimes.co.jp/news/?key=aomori1Whatever you decide, you need to trim it back by half. And get used to cold, even when there isn't snow.