Here's an idea. (But I'm no expert)

Wrap some of it with low voltage heating element wrap for pipes. Plug in when temp dictates. Cover it all with pipe insulation - the kind used for air conditioning lines.

Downstream, use larger diameter pipe, also wrapped, so it's less likely to freeze up completely before it drains.

One way or the other, you need to keep this pipe warm. Warmth can come from the surrounding earth, providing the pipe is buried below frost level for most of its run. Or, you have to provide heat, either by the use of heater cable or a hydronic line from a source of hot water.

No matter what, you are going to have to excavate a proper trench for this line. If the water is to exit into a ditch, then the exit point of the discharge line should be about six inches higher than the bottom of the ditch. Once you establish that, the bottom of the trench should rise 1/4" every ten feet until you reach the house. Therefore, if the ditch is 50 feet away, the trench will be 1 1/4" higher at the house than it is at the ditch.

That would be the minimum amount of "fall" in the pipe needed to make water run to the ditch while keeping the pipe buried as deep as possible.

Using electrical heating cable is a possibility but it's hard to find this cable in lengths long enough to wrap around the pipe for that distance. While it is probably cheaper and simpler, it would not be my first choice.

Instead, I would use four inch diameter PVC sewer pipe from outside the house foundation to the ditch. I would use transition fittings to allow the 1 1/4" discharge line from the pump to hook into the four inch pipe. I would then drill a one inch diameter hole into each side of the large pipe so as to allow a length of PEX tubing to enter one hole, run down the entire length of the pipe to the ditch and come back up and exit the large pipe. I would then seal those holes with a copious amount of silicone and let it cure for a day or so.

You now have a heating tube that runs the entire length of the discharge pipe. You could use one inch thick styrofoam insulation below, above and along each side of the pipe before backfilling the trench. The ends of the PEX tubing need to be long enough to go through a new hole in the foundation wall that is below grade. That way, nothing is exposed above ground.

A circulation pump designed for hydronic heating will be needed to circulate hot water from the water heater through this line whenever the temp falls below a certain level. You could control this pump with a simple on/off switch or you could add a timer to that switch. There are lots of options.

Electrical heating cables do burn out and that means you have to do the whole thing over again. And what if that happens in the dead of winter? The PEX pipe is tough and it is protected because it is inside the discharge pipe. To me, it is a "forever" system. If the pump should fail, at least it's inside where it's warm and easily changed out.

cast off, I will keep all that info for spring when we fix this problem for good I hope.

Maybe for now wrapping the pipe with insulation wrap and then putting that pipe inside a larger pipe might help to keep the pipe a little warmer.

Pitch the pipe corectly so it drains, and drill a hole above the pump but in the sump pit (1/8 inch usually does the trick) to allow drain back of the vertical leg of the pipe.
The water should not be in the pipe long enough to freeze.