Hokkaido in January by train?

I noticed that Hokkaido does have an extensive JR network; how well do these train lines deal with the snow that will be there in January? Are there parts of the lines closed during the winter or is everything kept open most of the time?

I once travelled by trains crisscrossing Hokkaido by trains in deep winter Feb 2011 for 2 weeks, no problem. All trains ran on the schedules, neither cancellation nor delay.

Thanks, that was indeed what I was after.
The countries were I lived would recently would quickly cancel trains and underground lines with the first flakes of snow.

I am not aware of any winter closures in the Hokkaido train network. But it does happen occasionally that train services get cancelled during snow storms. But then again, this can also happen due to storms during any season of the year. Hokkaido is generally well equipped for snow, otherwise, there would be no train service on the island, during winter, at all. The Hokkaido Shinkansen, too, was constructed with the large amounts of snow in mind:
http://www.jrhokkaido.co.jp/press/2015/150115-4.pdf