When you have a drought, it means the soil is very dry. When a storm system comes through, it will drop precipitation and moisten up the soil again. However, for drought-stricken areas, this precipitation must fall in a multi-day event for the soil to actually moisten up for good. Because of the dryness of the soil, when storm systems come through, the system will have no moisture to pick up from the soil, meaning that the system can dry up and weaken. It's a very vicious cycle, but unfortunately it does happen. Drought-stricken areas are naturally given a disadvantage right out of the gate when the winter starts.
Let's go back to the soil moisture issue, but let's say this is a sunny day. High pressure is over the area, but weak enough so clouds can form if provoked. On this day, we'll say that a weak cold front is moving into a drought area. Because clouds form by warm air (and moisture) being lifted off from the near-surface air, soil moisture does become an issue here. In a lack of soil moisture, less clouds form, and thus the sun stays out longer, slightly enhancing temperatures in the day. The lack of clouds at night enables the day's heat to be released back out into space, meaning that temperatures are slightly lower at night.
Those of you in this drought can expect a very slight lowering in precipitation and a very slight raising of temperatures this winter due to the factors I described above. These changes will not nearly be significant, but if you were to break it down into the decimals, you could see a small change.