I don’t freeze dough, so I can’t speak from experience, but if your dough is drying out, it may be due to a reduction in the air humidity that occurs in cooler weather, in addition to the longer rise time.
You might have better luck humidifying the air, rather than using oil. And I’m not sure that I would use a toaster oven to thaw and raise the dough. I have a hard time seeing that short bursts of intensely radiant heat is a good thing for the dough.
If I were to try this, I might be inclined to put the dough on top of a more gentle source of heat, such as a heating pad on low, and then cover the dough with a damp towel. Or cover it with plastic, but put a damp sponge on the inside.