On Monday night, conditions were ideal for temperatures to fall and fall dramatically in lowland regions. Tuesday night, things were different and clouds resulted in an increase in overnight temperatures overnight.
To illustrate this, let's take a look at observations from the Peter Sinks, a limestone sinkhole in the Bear River Range of northern Utah known for incredibly low overnight temperatures.
On Monday night, temperatures exhibited some ups and downs after sunset with some wild swings in temperature from about 1800 MST 3 Dec through about 0400 MST 4 Dec. Those swings occurred in conjunction with gusty winds, which occasionally mixed out the cold pool that was forming in the Sinks. However, after about 0400 MST 4 Dec, the wind died down and temperatures fell nearly continuously, reaching a minimum of about -35˚F at about 0900 MST 4 Dec when I suspect the low angle sun finally began to warm the sink, after which temperatures rose until the early afternoon.
Last night, however, things were different. The air was mainly calm all night and the temperature fell nearly continuously from about sunset through midnight (0000 MST 5 Dec), when it reached an incredible -40˚F.
However, after midnight something remarkable happened. The temperature increased 35˚F, reaching -5˚F by 0700 MST 5 Dec. This happened despite it being night time and the air being calm or nearly calm. Similar temperature traces can be found at many stations in northern Utah, although as you move southward, the temperature increase occurs earlier. For example, at the Clover Site in the Rush Valley southwest of Salt Lake City, which is also known for very low overnight temperatures, the minimum temperature occurred at about 2000 MST 4 Dec, after which the temperature rose until this morning .
Overnight several things happened. First, cloud cover spread over the area, as can clearly be seen in the overnight satellite imagery.
Second, cloud base lowered. At the Salt Lake city airport at midnight (0000 MST), a few clouds were reported at 20,000 feet above ground level, but by 0400 MST, the broken clouds covering 6/8 of the sky were reported at only 3700 feet above ground level.
Finally, those clouds accompanied an elevated warm front that moved through the area and increased temperatures aloft. Yesterday morning, the 700-mb (about 10,000 feet above sea level) temperature was -14.5˚C.
However, this morning the 700-mb temperature was -7.5˚C. Note also that while there was an inversion yesterday morning from the surface to 850 mb, the atmosphere was relatively well mixed in that layer this morning (although the inversion based at about 800 mb and associated with the warm front still puts a lid on the valley atmosphere).
So, overnight free-atmosphere temperatures aloft and at mountain elevations increased, but so did the cloud cover. I suspect that the latter played a critical role in rising overnight temperatures in cold spots like the Peter Sinks. With the air calm, it would be very difficult to mechanically mix out the -40ºC cold pool that had formed by midnight. Instead, the cloud cover was probably critical.
Clouds are important not because they "act like a blanket" (they don't), but because they emit infrared (longwave) radiation. On a clear night with dry air in place, there is very little longwave radiation received by the ground (or snow) from the atmosphere, and temperatures plummet. However, on a cloudy night, the incoming longwave radiation is greater. How much greater depends on the temperature at cloud base, with low, warm clouds emitting more longwave radiation than high, cold clouds. This radiation is then received by the Earth's surface or the snowpack, which cools at a slower rate than would occur under clear skies.
Last night provided an extreme example of this in which clouds actually produced increasing temperatures. In Peter Sinks, temperatures were -40˚F (which equates to -40˚C) before the clouds spread in. Based on this morning's sounding above, the temperature at cloud base by this morning probably reached at least -10˚C and perhaps as high as -6˚C. The amount of infrared radiation emitted by the clouds and also by the snowpack strongly increases with temperature. Thus, with much warmer clouds spreading over a cold snowpack, the snowpack would begin to receive more longwave radiation than it was emitting, and would begin to warm. That energy subsequently is transferred into the atmosphere, resulting in an increase in the near-surface air temperature.
This process really has nothing in common with how blankets work. Blankets keep you warm primarily by reducing the mixing of air near your body with the air farther away. This keeps relatively warm air near your skin, reducing the transfer of heat to the atmosphere. Clouds don't directly affect the transfer of heat from the Earth's surface to the atmosphere. They affect the temperature by changing the radiation balance and providing more longwave radiation than clear sky.