"Obama just doesn't inspire me that much" and "bad weather" are simpified stories someone might tell to explain their behavior. But "Does Obama inspire me enough to deal with the bad weather?" is closer to how the decision is made.

Do you think Democrats and Republicans are different enough that their algorithms for dealing with bad weather differ in a consistent way?

I would not rule out their being some correlation with willingness to go out in bad weather.

I could imagine a world where Democrats and Rupublicans really run the same algorithm with different parameters pointing to different political entities that are close analogues of each other, in which case a Democrat would acausally influence Republicans as much as Democrats. But this does seem to be a highly specific hypothesis, that I would not favor, and does not fully fit in with actual assymetries that can be observed.