Where I'm planning to hide it, it won't be an issue. Also, the glass is pretty thick. You could likely drop it on the ground and it wouldn't crack. It won't just be lying on the ground somewhere or where a raccoon or some other animal could get to it. I could test the freezing temps thing in my freezer, it's an oil so I don't think it'll freeze meaning it shouldn't expand/contract depending on temperature. I moded it also so the inside where the liquid is, is completely closed off so it won't spill/leak/etc. There's a plastic tube that is inside it that keeps the log dry and it's using a wine cork to keep the inside dry.
I should refine what I typed above. Oil can freeze, it just doesn't freeze at the same temperature as water would, so it should be a lot better in the cold. These are kind of just concept caches though, I could switch them up with candle wax if it does have issues when I do the freezer test run.