Word travels pretty fast, especially since the weather would have been mentioned on any radio or internet weather report, seeing as snow piling up in Kyoto is pretty rare. People may have even traveled out to see it, only to quickly flee when they realized it was just continuing to pile up.

Likewise, the trains getting stopped up would have a noticeable ripple effect, since Kyoto is very much a hub for other stations. The snow may also fall in nearby cities, but not to the same extent as Kyoto.

In other words, unless you live under a rock, anyone in Nippon would have some idea of what is happening.