This Summer I installed an 18000 BTU Air Conditioner in a living room window. Will it harm the unit if I leave it in the window for the Winter? I live in Minnesota.

It is very commonly done, at least here in a little milder climate. Many people put a cover on the outside, but that is mainly to keep cold air from working its way through the unit. It might be a good idea to read the manual or check with where you bought it.

Nobody brings the compressor unit for central air inside in the winter.

Thanks for your help

Hi,
The cover for the window air conditioner is a "must" have. You also might want to check around the air conditioner, where it comes in contact with the window frame, looking for any air holes. If you find anywhere that air can get through, you might want to cover them with some type of insulation.
Sometimes, even the cover itself doesn't completely cover up some of those areas.