I took the opprtunity to fill the bird bath knowing there is a hard limit for freezing of 32F. It did not freeze over (too much volume, not enough time below 32F I guess), but unexpectedly dew on the car windshield did. Frozen water test is good for calibrating or testing termometers, so it proves the cheapo termometer can be off by 3-4 degrees maximum.
Actually you have the clues here but perhaps lack a bit of background? Pure water freezes at sea level at 32F. There's a variety of factors that may be at play here, which you'd have to weed out.
Pressure plays a role. During the cold spell perhaps the atmosphereic pressure was changed in such a way it enabled water to freeze at a slightly higher temperature.
Contaminents can play a role. Even if you 'cleaned' your window the night before you would have dirt or lint on the windsheild. Again perhaps the right combo to bump the freezing up slightly.
And yes amount of water can play a role. Water is densest at about 39 degrees. Microscopically ice crystals can begin forming as the density changes with the drop to 38. If you have a very slight amount of water, windshield vs bird bath, you might possibly find a thin layer of ice.
Another effect possibly at play is supercooled water. Water can remain a liquid down to about 29 degrees. If you have a rain drop or two hit your windshield the energy imparted to the rest of the water may be enough to freeze it instantly. Freezing rain is an example of this.
The other thing that can happen is that colder air is more dense and closer to the ground. If it's a calm night the earth may radiate heat in to the atmosphere as the cold air settles closer to the surface. If one thermometer is in a valley and the other on a hill the will read 2 different temps, and both be correct. This effect leads to conditions that surfaces, car window is a good one, will lose heat quickly and actually be colder than the amosphere.
Any, or all, of these might be possible. If you want to know why, why not call one of the weathermen up and ask? I know our Public Radio Station takes questions for the weatherman whose actual job is working for the University of Minnesota.
Here's a decent read I found (tried to use Google to find this effect)
http://www.wral.com/weather/blogpost/1183613/