The sad fact is that even with little headroom, there is probably more O2 dissolved in the PG or VG than in the mL or so headspace. Freezing VG-nic will essentially stop all reactions, since it becomes almost glue-like in the freezer, and the nic or O2 has little mobility. PG-nic might not fare quite as well, but it depends on the liquid itself. TW 36 mg PG unflavored deepened a lot and became very tobacco-tasting after a year in the freezer. Decadent Vapor, which uses higher grade purer nic in PG hardly changed at all in a year. PG-nic is still quite liquid and mobile in the freezer. My VG-nics have not changed at all in 2+ years, and I do not expect them to.
that all said, the amount of O2 that is in a glass bottle of nic-liquid is very small, and even if it all reacts, the potency of the nic will hardly be diminished. Also, while the TW had changed dramatically in a year, it had changed into an absolutely delicious tobacco-flavored liquid. I was sad that I had to give it away, but PG causes big problems with me. If I could replicate that flavor in a VG juice, I'd be in heaven.
Glass is more stable to long term liquid storage. Also PG and VG both can leach plasticizers from some plastics, which is not good for you, and leads to cracking over time. Which plastics, I do not know, so I just store long term in glass.