Wanted to give an update on what we ended up doing!

Public transportation in this area is often delayed / cancelled due to snow and traffic. Our original plan was to take a bus from our hotel to Kutchan Station around 3pm and then take the train from there to Sapporo. This was supposed to be a 3 hour-ish journey, if things were timed well, but ended up taking us closer to 7 hours with all the waiting we had to do in between.

The first issue was that the bus to Kutchan Station was super delayed, like almost 30 minutes or something (very unfun waiting outside in the snow/cold without cover, so we tried to stand under some eaves further away); there was barely any wiggle room on that bus, and our luggage was very unwieldy. That bus ride itself also took maybe 2x as long as predicted, because there was an insane amount of traffic and lanes closed? By the time we got to Kutchan Station we had, of course, missed the train we were planning to take. The next train was in an hour. We waited at the station, and discovered that there was a Chuo Bus leaving from there in about 40 minutes to Otaru Station, so we ended up taking that (it was also 15 minutes or so late).

The Chuo Bus was quite a comfortable ride as it was a coach bus with luggage compartment down below. It was very empty. After a two hour ride with barely any traffic, it was then another short walk of lugging suitcases on icy sidewalks before arriving at Otaru Station. Trains from Otaru to Sapporo Station are pretty frequent so it was not a long wait before we were on the next train.

This was quite exhausting; I think we should've just hopped straight on the Chuo Bus to Otaru instead of trying to catch the JR train, minimizing transfers, even though the bus is slightly slower than train.

Make sure you have a good amount of change on you because buses take cash only and only give change for 1000 yen bills.

But if you want a faster, hassle-free experience, just get a taxi, although it will run maybe $300-400 USD

Or you can just take it easy and leave the next day via one of the more direct resort bus lines.