They (old Rhizomes) do go brown and corky, not only in winter but at any time of the year, I don't know what causes it, could be old age, a pathogen, or something I know naught about, but the main rhizome dies by degrees, leaving only the new growth points, which also die if the rot is not cut out. The new growth points strike readily enough in Sphagnum and are kept wet, but if you catch it early in the main rhizome, where it starts, normally where there are no growth points, generally at the oldest part of the rhizome, a simple cutting out of the corky bit to healthy growth and pot up in new medium, does the trick.
Most of mine sit out in the UK all year, including seedlings, so get frozen and are normally quite happy (apart from minors, psittacina and rosea that seem to be more tender and have a tendency to rot), but they do occasionally get rot. It's the ones I mollycoddle in the greenhouse that seem to get it worse, whether that's because they are softer, I don't know.
Cheers
Steve