A significant snowstorm is possible Tuesday for at least parts of New Hampshire, according to the National Weather Service. If the greatest impacts are along the coastal areas of the state, as is currently possible, it could impact turnout in areas of the state most receptive to 'establishment' candidates such as Rubio, Kasich, Bush & Christie.
At this point, the Weather Service sees snow 60% likely in Manchester and most areas through the state. Of particular note in the latest synopsis is that "there is potential for this system to become a significant snowstorm late Mon(day) through Tue(sday) for Maine and New Hampshire...especially along coastal areas".
Why would this hurt Rubio?
The graphic below, from The Wall Street Journal, attempts to project how candidates will do in different parts of New Hampshire, based on results from Iowa. Rubio's strong areas look to be more metropolitan areas and college towns, with the other establishment names expected to do well in the metropolitan areas. In New Hampshire, these areas are concentrated in the southern third of the state, the area most likely to see the greatest impacts from this storm. To the extent this hinders turnout in those parts of the state (relative to the more inland regions), Trump and Cruz could be the beneficiaries. At this point, Trump remains well ahead in the polls, with Cruz and Rubio in a battle for second.
Lots of caveats here: New Hampshire is a primary not a caucus, the characterizations in the graphic may not neatly transfer from Iowa to the Granite State, the evolution of the race may overwhelm any weather-related impacts and, of course, the state's residents are used to harsh winter conditions so turnout may not change all that much.