The fundamental difference between the two nights was the presence of overcast skies for much of the night last night.
|Overcast skies ruled for most of the night and early morning|
over the Salt Lake Valley. Source: George Wilkerson.
Blankets slow the transfer of heat from you body to the atmosphere by reducing the mixing of air and the size of the temperature gradient near your skin. The opposite occurs when the wind blows across exposed skin, which increases the mixing of air and the size of the temperature gradient near your skin, increasing the transfer of heat from your body to the atmosphere and making it feel colder.
On a cloudy night it is warmer not because of clouds affect the transfer of heat between the Earth's surface and the atmosphere, but because they affect the net radiation at the Earth's surface. On a clear night, the primary sources of downwelling radiation at the Earth's surface are greenhouse gases, especially water vapor. On a cloudy night, clouds provide an additional source of downwelling radiation. As a result, the net loss of energy at the Earth's surface is smaller, the temperature drops more slowly, and the minimum temperature is higher.