A warm winter will, however, cause consumption of natural gas and home heating oil to decline.
I'd expect that the number of miles driven commuting to work is driven by both the economy and also gas prices. When gas prices rise, more people find public transportation a better alternative. The general economy can affect miles driven by having more or less people having jobs to go to. I doubt that warm or cold weather would change the number of miles driven for commuting one way or the other.
Miles driven for purposes OTHER than work are probably more related to personal finances (particularly the effect of high gas prices) than how nice the weather is any particular day.