Partially frozen sewer line
I would start with boiling water - a couple of very large pots.  Dump.  If you get any kickback or notice that your water levels stay high repeat a few times.  If you have ice or a blocked line, really hot water helps both.  

Normally you would check your water levels in a cleanout or basement drain - from the sounds of it you have a bathtub at your low point or maybe it is at the same level.  Usually I tell people to have one person look with flashlight on drain.  If you see the water levels rise, even a little temporarily then usually there is some sort of blockage - I know that it may be ice in your case.

If the water isn't backing up into tub move on...

Then I would fill showers/sinks/tubs - anything that holds hot/scalding water and fill them until you run out - except for said tub that got the backwash.  Again good to have another person at tub/drain.  Dump everything at once.  If it starts backwashing to tub then stop.  You have to think just after a few times doing this that ice would be thoroughly melted and then you need to troubleshoot like your main line is clogged.