Training Status such as "Unproductive" is calculated on your Garmin hardware device. Garmin Connect only displays what the device calculates. (I think that is a flawed approach, but Garmin is primarily a device company so that's just how it works.)

If you know that you're going to be running in challenging conditions like snow that reduce your pace then use the Trail Run activity profile and set "Record VO2 Max.” to Off. That should prevent it from changing your fitness metrics.