Is temperature-dependent wind resistance the reason there's a significant increase in fuel consumption in my Prius car when air temperature drops by 30 degrees K from 300 degrees K? I think I see a similar effect when riding a bicycle. At constant pressure, air density is inversely proportional to temperature, so density has increased by about 10% in winter correct?
Yes, the increased air density in winter will increase drag and thus fuel consumption, especially on the highway. The density is increased by even more than the 10% you propose, since the air is usually drier in the winter than in the summer, and dry air is denser than wet air (because the molar mass of N2 is much greater than that of H20). Also, the viscosity of air is increased in winter. Thus drag is much greater in winter for several reasons.
There are several other factors which tend to reduce efficiency in the winter, including:
Massively increased viscosity of engine and transmission oil (this is why older cars took thinner oil for winter than for summer)
Increased stiffness and internal energy dissipation of tires
Reduced tire pressure if you haven't filled them since summer
Reduced battery current at lower temperatures, necessitating more frequent charge cycles
...and I have probably only scratched the surface of the detrimental effects at play. Everything gets harder in the winter!
I think you are right about the 10% increase air density in the winter and this thorough answer on the Bicycle Stack Exchange supports your observation about the effect when cycling.
Drag forces are directly proportional to air density so that would have an effect on fuel consumption. There is another factor this is also significant - in regions where there is a wide variation in air temperature throughout the year the blend of gasoline changes seasonally as described here: Winter vs Summer Gasoline… yes there is a difference. Winter gas is more volatile, easier to start but less energy dense resulting in increased fuel consumption in the winter.
Also, the efficiency of the battery in the Prius decreases with temperature below 70F. Here's a study.
You said "at constant pressure." I think you mean without wind, correct? (Because you also mentioned wind.) Just so there won't be confusion let's remove wind from the equation and assume the air is completely motionless at colder temperatures.
Air molecules condense or shrink in cooler temperatures - causing higher pressure. So yes, cooler temperature requires more energy to move through compacted air.
Wind is something different. It is moving air molecules. Which is at least partially caused by temperature changes.