If you want to focus on the lack of brightness:
* Dull: The dull skies ushered a gloomy winter day.
* Gray: The gray skies ushered a gloomy winter day.
* Overcast: The overcast skies ushered a gloomy winter day.
If you want to focus on the sense of desolation:
* Desolate: The desolate skies ushered a gloomy winter day.
* Barren: The barren skies ushered a gloomy winter day.
* Despondent: The despondent skies ushered a gloomy winter day. (This is a bit more figurative, but still captures the feeling)
If you want to focus on the coldness:
* Cold: The cold skies ushered a gloomy winter day.
* Chilly: The chilly skies ushered a gloomy winter day.
* Freezing: The freezing skies ushered a gloomy winter day.
The best synonym will depend on the specific nuance you want to convey.