In my municipality, it's illegal to run a drain line into the city sewer system. What's suppose to be done is it's to be run directly outside or to a sump. You can put a bucket under the end to see how much water comes out in a day and if it's not too much, you can temporarily divert it inside until you come up with a long-term solution. You just can't forget about the bucket or you'll have a new problem! If you do this, install a 'T' connection that you can turn on and off at a whim. When you have a final solution, tape the 'T' valve to whatever position so no one turns it on/off on you.
If you have a sump, just run the line to that. Test the sump first to be sure it will come on. Run a hose line or dump a few buckets of water in it to be sure the unit is operating.
Usually, if there's a 'steep' enough drop in the line when it gets outside, the water won't freeze because it's moving. If you line is laying pretty much in a flat line, see if you can re-work it to have more 'drop' in it. It should terminate at least 3' from the foundation. You may be able to insulate it on the outside of the house a little to help keep the water from freezing. If the line is 1/2", there's 1/2" pipe insulation at any Home Center. I've never seen it or done it but it's worth a try. My best to ya and hope this helps.