How does a Drought affect the coming winter?

A drought will affect the amount of water vapor in the atmosphere and soil (no kidding!). Water acts in two ways to moderate temperatures in the winter. First, it acts as a greenhouse gas, trapping outgoing longwave radiation and reemitting it back towards the surface. Second, the amount of water vapor in the air determines the hypothetical absolute minimum temperature at night. The dew point temperature is the temperature at which saturation of the air and condensation on surfaces (dew if liquid, frost if frozen) occurs. When water vapor condenses, it releases heat, and keeps the temperature at the surface from dropping below the dew point much, if any. However, the lack of water vapor may also mean a lack of clouds (though not necessarily is this always true). A lack of clouds will allow more sunshine to reach and warm the surface. In any case, if the drought continues through the winter months, you should expect more drastic temperature swings from the day to night time. The lack of clouds will help to warm the surface during the day, but cool the surface at night, while the lack of water vapor will additionally increase surface cooling at night. The three factors combined probably won't alter the average temperature that much for the winter season, but it is likely to cause more extreme temperature events (record highs and record lows).