Pull the starter relay and reseat it, look for corrosion on the contacts, if not that then may possibly be the Park/Neutral safety switch sticking with the colder weather.
Just went through this with my wife's car this past week, starter was fine. Next time it does that, try moving the shift lever back and forth see if that resolves a start.
See if it will turn over when you place it in neutral. If stranded and all else fails, put key in run position and jam a screw driver in between the contacts on the starter. (make sure no fuel leaks nearby)
I'm assuming you have bright headlights when this happens. May also try knocking the starter housing with a hammer while someone else turns it over.
fun fun fun.