At around -5F here this week, I'm not doing any riding. The Port Dover Friday 13th bike "rally" was last week, I saw some biker types walking but no (zero, nada) bikes when I checked their street webcams. One (mentally defective or masochistic) fellow supposedly did go on a bike - but it was a Ural 2WD sidecar rig. Around here you can deal with snow if super careful - it's not much different from loose gravel or dirt - but ice is nasty and freshly laid salt is like being on marbles. There are a few dual purpose bikes out in the area once the roads are clear and dry but not when snow is falling or after when the roads are salty slush.
For frozen cables... if you can push it to heated parking or a service bay, once it warms up and they can move shoot a bunch of WD40 through the cables followed with cable lube or light oil. If it isn't caused by water freezing, then whatever lube is in there is turning to rock when cold. The stuff in WD40 gets pretty thick when cold, I use motor oil myself for lubing cables.