A downpour not only brings the heavy rains down, but can bring down colder air from higher elevations along for the ride. That can artificially drop a snow level a good 300-600 feet or so, changing what was a heavy rain into snow.
This happens a lot during Convergence Zones on cold days. A heavy shower turns to snow in Lynnwood, only to have it melt soon after the storm subsides and the snow level returns to its higher level. Heavy showers can also temporarily drop snow levels in the passes to the surface, making for treacherous driving.