In my house the furnace/AC is on the second floor along with the washer/dryer. I had a whole house humidier installed and the person who installed it, drained the excess water from the humidifier into the washer drain. A few months ago, I replaced the plastic tubing and didn't have enough so I drained it into the plastic piping that goes from the A/C to outside (condensation drain?). Any way that was a bad idea as, even though the water coming out of the humidifier is a trickle and warm, the pipe outside froze (it's been very cold the past two weeks) and the water backed all the way up to the second floor and overflowed. I don't know how long it took for that to happen as it's got to be at least 30 to 40 feet of pipe, but there were icicles coming out of the bottom of the outside piping. The piping, which is plastic PVC, comes out horizontally about 4 feet above ground and bends vertically and goes down another foot or two. I have no idea where it goes once inside the house as it comes into the (finished) basement wall, but it either goes up or across the outside wall for at least several yards.

I caught it shortly after it backed up to the top so no more water is going into the pipe and I siphoned out as much water from the second floor pipe as I could so the water should no longer be backing up into the A/C unit drain, but there's still water sitting in the pipe (I've confirmed this) as it won't drain to outside.

Today I successfully thawed the piping outside the house (took a long time), but the water isn't draining. It appears to be clogged somewhere inside the house, presumably with ice. I tried forcing warm water up the outside pipe as best I could, but the same amount of water came out as what I put in, so if there is ice, the warm water is not reaching it. The outside temperature is only 37 degrees today, but I wouldn't think the water in the interior piping would be frozen. Then again recent nightly temperatures have been in the single digits. The pipe doesn't appear broken since water from upstairs isn't draining, but I have no way of really knowing until the water starts draining.

Is there something I can do at this point or do I need to wait until it warms up outside?

You might as well open up the affected wall and ceiling portion because the line is probably broken anyhow. It takes very little pressure to break pvc, and freezing water is more than sufficient to do the job.

I would slide a small plastic tubing into it from the outside then run hot water through it. You want enough pressure for it to go up the pipe as the ice thaws.

The outside pipe didn't crack and that had a solid block of ice in it. I'm actually not sure if it's pvc. It's plastic and an inch in diameter the wall around 3/32 of an inch. The pipe says SDR-21 200 PSI 73 degrees F on it.

In any case it runs through the foundation and then sort of disappears into the wall. I wouldn't know what to tear open.

I tried that with 5/8 inch tubing, but it wouldn't take the 90 degree bend. I guess I can try a smaller tubing.

You may not need to turn the corner. You just have to use enough pressure to force the water up the pipe.

I don't have a pump so I was using gravity with one end of the tubing being higher than the other. It didn't appear to be good enough as only the water I put in, came out. I tried multiple times and it never reached the ice still currently blocking the pipe, assuming it is ice.

You need to hook it to a hot water faucet to get enough pressure to do any good.