Does the game try to beat you up badly, until your population dies eventually. It might sound like a stupid question, but I want to make sure I can enjoy playing that mode the way I can play Banished and Tropico 5. That means I would like to play the scenario indefinitely, if my city meets the requirements needed for self-sustainable survival, that is.

Yes, it is endless. The weather cycles stop getting any worse after about 30 days, which means if you survive that long you can basically survive indefinitely. If you're playing for a challenge there's not much point to continuing other than the achievements, but if you just want to build you can do that as long as you like.

Thank you for reply.

Darn.. was hoping for a secret story ie the cold ends, you find out the cause of the great winter etc

Unfortunately this does not seem to be the case. After a while you'll start experimenting with various ways of having the camp laid out, discover that you're never finding any more steam cores or survivors, so you don't even end up in an over population situation. I think my largest endless camp has enough raw and cooked food, as well as coal to outlast a 60 day storm (with food being the problem there). At some point you're basically just watching the timer fly by while you do a minimum amount of input to keep the population from wanting to overthrow you (can be done without going to extremes), and I don't find that particularly interesting.