Will save files made while using Windows 7 work properly on Windows 8? I think it shouldn't cause problems, but I'm not sure. I'm going to change my OS and I'm afraid that my saves and all progress in Skyrim could be lost. What do you think about it?

If you had Steam Cloud sync, it should be fine. I currently play my old save from W7 on my new PC which is W8 without any issues.

The game determines the file format for the saves, not the OS. As long as the game version is the same or greater than the other one and you're using the exact same mods, there should be no difference.

Thanks for your answer, Patriarch- I'm calm now