Typically, how big a temperature drop do you get during a total solar eclipse?
It would probably be equal to the typical daytime minus nighttime temperature difference at that time of year and location on the Earth. It would be modified a bit by the fact that it only lasts a few minutes, which means the environment would not have had much time to thermally respond to its lowest temperature, so it would probably only be 3/4 or 1/2 the maximum day-night temperature difference. Because the patch of the shadow travels faster than the speed of sound, weather systems will only be affected very locally directly under the instantaneous footprint of the eclipse. The main effect is in the "radiant heating" component which goes away suddenly at the moment of eclipse and produces a very fast temperature decrease. If the wind is blowing, your body probably exaggerates, by evaporative cooling, how large the actual temperature swing actually is.