In a thunderstorm cloud, you're extremely unlikely to encounter free protons (or electrons). What you get is that some of the molecules (that themselves will be assembled into water droplets) in there will gain an additional electron, making them negativel charged, while those that have lost them will be remain with a positive charge.
Only when the lightning discharges you will get free electrons and highly charged atoms, making up the plasma of the lightning.
Electric flow is even more complicated - in a lightning discharge, it's in the plasma. In a solid (like a conducting wire), it's electrons - but not free electrons. Basically, all the atoms in that wire together share a pool of so-called conduction electrons that can move more or less freely throughout the wire. So conductivity in a solid is more of a property of the solid as one of the individual atoms - those contribute by having losely bound outer shell electrons, though.