From the National Weather Service in North Platte:

A strong low pressure system will cross the Central Plains Tuesday. This system will bring with it snow, strong winds, and blowing and drifting snow. The heaviest snow and greatest impacts from this storm will be along the Kansas-Nebraska border, then eastward into southeastern Nebraska. The Interstate 80 corridor in southwestern Nebraska will be near the northern end of the heavy snow. This means that Imperial, North Platte and Broken Bow may receive anywhere from 4 to 8 inches of total accumulation, while Ogallala, Thedford, and Oneill will only get 3 to perhaps 6 inches of snow. Meanwhile, over 8 inches of snow will fall in the Grand Island and Lincoln areas.

This will be a fast-moving storm system. The snow will not begin until later tonight, and will not become heavy until Tuesday. The winds will pick up about midday Tuesday.  However, the system will move out of the area by Tuesday night, leaving very cold air in its wake. Wind chills could be 20 below zero or colder by Wednesday morning.