Yes, I guess it could, but it depends on what's in it.
Generally, a VG
juice will contain water at somewhere between 10-20%, plus nicotine and flavourings. For example, a mixture of glycerol (80%) and water (20%) freezes at -19.2 degrees C (
source). Note this is much lower than either water or VG on it's own. I don't know what the exact freezing point would be for mixed liquid with flavourings and nicotine in, but my guess would be a VG
juice would freeze at the kind of temps you are talking about (-40F = -40C).
PG is used as a component of some (safer) antifreeze's and freezes at -59 degrees C. A PG juice would likely not have more than a few % water in it. So, I think a PG juice would be more likely to not freeze at -40 degrees.
Whether you could practically use an e-cig outdoors in such cold conditions is another question though! I have tried in temps down to about -10C and it worked but nowhere near as well as indoors.
