Let's start with the clouds. It is often said that clouds act like a blanket, but this is a terrible analogy if ever there was one. A blanket keeps you warm because it prevents the mixing of air near your body with cooler environmental air. This slows the net loss of heat from your body to the atmosphere. In contrast, clouds contribute to warmer nights by providing an additional source of energy to the Earth's surface—namely infrared (a.k.a., long wave) radiation emitted by the clouds themselves. Often it is said that clouds "trap", "reradiate", or "reemit" radiation coming from the Earth's surface, but this is also an oversimplification that is somewhat misleading (we will save that discussion for another day). With this extra source of energy, the Earth's surface cools at a rate slower than it would on a clear night. All else being equal, low clouds usually result in warmer nights than high clouds because low clouds are usually warmer and thus emit more infrared radiation.
Now on to wind. On a calm night, there is typically very little turbulence to mix the air near the Earth's surface. As a result, the cooling is concentrated in a very shallow layer and temperatures fall dramatically. Sinkholes and basins often observe the lowest overnight minimum temperatures as they become very calm at night. Wind generates turbulence, however, and instead of forming a shallow layer near the surface with very cold temperatures, you are constantly mixing the air, leading to warmer conditions near the surface.
So, last night with extensive cloud cover and strong winds, we simply didn't see temperatures drop as they do on a clear, calm night. Thank the radiation from the clouds and the mixing from the wind.