We have maybe 8 inches of snow and I don't recall how deep the line is. I think it's about 3 feet but could be more....or less. I'm hoping it froze right where it goes into the ground but I doubt that's the case. Too steep an angle at that point.
Here is the weather pattern that I have become used to. Cold October/November. Big snow dump just before Thanksgiving. Then a warm spell of 4-5 days, might even thaw a little. Week before Christmas gets really cold and hangs on through mid/late January with continuous small snow storms. February is nice. 40-60 below at night 10 below to zero during the days. Sunny and bright....except at night.
Your results will vary.
Well, I can see you have a few options :..
1. Are you hooked up to the City Sewer or private Septic System ?
If it is a City sewer , I would call the DPW and tell them to start digging . Think "HEALTH & SAFETY" !

that usually is the only way to get the DPW to do anything this time of the year.
2. If you can get into the frozen in pipe area where it is under the house, assuming you have a Crawl Space with enough room to get around in, you might try wrapping the frozen pipe with electric pipe heater tape to warm up the pipe and free the clog.
3. Got any RV Antifreeze to pour down the drain ? That MIGHT work.
4. In the Spring or Summer, dig up that area , wrap the pipe with insulation and that electric heater tape and bury it 1 Foot below the Frost Line. That is really the only way to prevent frozen Sewer Pipes that are buried underground.
5. Another option would be to use Spray Foam insulation around the buried pipe. In the Summer, dig up that pipe and spray the foam insulation in the trench where the pipe tends to freeze up. Spray enough of that insulation in the trench so that the pipe is completely covered . I would say at least 12 inches of insulation would work well around the pipe.