How to extract the filename without the extension and write that to a tag using ExifTool?

Make sure you're using exiftool ver 12.22+ and change Filename to BaseName.

exiftool '-Comment<BaseName' winter.mp4

If you have to use an older version, you can use regex to remove the extension

exiftool '-Comment<${Filename;s/\.[^\.]+$//}' winter.mp4