It's not that good of an idea to freeze pre-mixed juices ....the different ingredients (nicotine, PG, VG, flavorings) can freeze then thaw at different rates.
Aqueous substances in solutions don't usually freeze at different rates in solution. That's why your car's radiator doesn't turn to slush in winter but stays liquid. Glycol based solutions also don't usually expand so you shouldn't have to worry about a glass bottle (or your car's radiator) blowing up in the freezer either.
Unless you have juice that is over 90% VG you aren't going to freeze the juice in a home freezer as the freezing point of the juice will be below 32F. You're just going to be cooling it.
90+ VG is an exception though as Pure Glycerin (VG) has a freezing point in the low 60s F, which is why it's so thick at room temp. You'll want to keep a truly 100% VG juice above 70F at all times. But just a little bit (around 10%) of PG, PGA, or water will cause the freezing temp of the solution to drop drastically making it safe to store in your freezer (and a bit more viscous at room temp). But 100% VG juices are fairly rare as most flavorings are PG or alcohol based and VG. If you can get the juice out of a typical dropper bottle at room temp (72F) it's probably no more than 90% VG and likely safe to put it in the freezer.
Just don't flash freeze it, drop in liquid nitrogen or put it in front of the cooling fan in the freezer and you'll be fine (quick freezing can defeat the anti-freeze properties of the solution in spots and cause crystallization which is bad). The best thing is to first put it in the door of your fridge, then after several hours, move to the coldest part of the fridge. Then the door of the freezer. Then to it's final resting area. Cool it as gradually as you can.
And when you take it out the freezer, do the reverse. Warm it up as slowly as you can. Fast thawing is as bad as fast freezing. And don't shake it or agitate it until it's warmed to room temp as that could cause crystals to form. And as it'll usually be the flavoring which forms crystals, that's what is most affected if it happens.
After it's been at room temp for a few hours,
then give it a good shake in case there was any separation while it was chilled. You may also need to resteep it if it's a juice that normally needs to steep.
Chilling will definitely inhibit enzyme reactions which
will extend the life of your nic and most flavorings. So it's not a bad idea if you're going to be storing it for a long period of time. Just remember to cool it and thaw it as slowly as possible and minimize agitation during temp changes and it's a good idea.