A fast moving area of low pressure is currently in western North Dakota moving to the east/southeast. This low will bring a band of rain and snow along and north of the center of the low as it moves across North Dakota and Minnesota.
The High Resolution Rapid Refresh (HRRR) model seems to have a good handle on the evolution of this system during the day. With a band of snow near and north of Highway 2 with some rain mixed in closer to interstate 94. Because the precipitation is coming in during the day, plus, temperatures are not that cold, the snow accumulations should be held down. Most locations in the snow band will probably record around 1 inch or less with some localized locations in the heart of the snow band getting around 2 inches of snow. Because the snow will be gone before sunset, some melting of the snow will not only occur as it is falling, but also after the event through sunset. Although Saturday does not look especially mild, it still looks warm enough for the snow to finish melting tomorrow.
On Saturday a ridge of polar high pressure will briefly move into the state, but then on Sunday another fast moving area of low pressure from Alberta will move into the area.
On Sunday as another disturbance passing through North Dakota a more widespread light snow event is expected. It may mix with rain at times, but it appears most locations will record mainly snow, albeit light snow during the day.
After a break and a brief warm up on Monday, yet another system, this one coming in from the southwest will bring a mix of rain and snow to the much of the upper Midwest on Tuesday into Wednesday. That system at the moment seems to have the greatest potential for high precipitation totals.
Therefore, it appears there will be 3 threats of rain and or snow across North Dakota through the middle of next week. Tentatively there may even be a 4th next Friday or Saturday. But with these systems all having enough cold air for snow for at least some locations, obviously, no significant warm up is foreseen. The rest of the month will see more days at or below average than above it appears. With multiple threats of precipitation.