Every morning I ride my mountain bike and every morning - especially when it's really cold (really cold to me is below 55 degrees) - my nose starts to run and/or drain. Am not sure that there is much of a difference. However, it's gotten so bad, that I end up shooting "snot missiles" every 20 minutes or so.
I wear contacts, so using an OTC pill to dry up the nasal passages will also probably dry out my eyes.
Any other suggestions (other than wait till it gets warmer - have done that and it still happens, just not so often) would be appreciated.