We've just had a bad cold spell, including temps down to 9 deg F 2 consecutive nights and 12 last night. Temps this low are very unusual here, the lowest I can recall in 17 years here (Corvallis, Oregon), where we may get snow once a winter that usually is gone within a day or 2.

I have left water trickling in 2 sinks each night.

Yesterday morning the shower and toilet worked fine at first, but as I showered, the water backed up in the tub, then drained out without any help before I finished. The toilet was bubbling and overflowed when flushed once. The rest of the day everything worked fine

Today the water didn't drain from the tub, so we didn't flush the toilet. Late this afternoon I bailed out the full tub, then began pouring boiling water down it's drain. (The water level in the toilet went down as I bailed and it went up slightly when I ran the kitchen faucet.) It finally drained, so we flushed the toilet--and had a mess to clean in spite of plunging. And the drain is not working again. I've continued with the boiling water and it finally just went down again after sitting a while, but now it's bed time, so we'll leave it until morning.

Is this likely a problem with the vent that I read here?
Temps are rising to around freezing... hopefully it will fix itself.
If not, can we pour hot water into the vent? Do we need to use a hose?