I am not OP but I moved to Santander in March 2022. I love it!
I don't consider it depressing or grey even though I'm subject to winter blues.
Yes it can be cloudy and overcast and it does rain more than most other parts of Spain.The winter sun is lower in the sky as well.
I can't take the heat and humidity of Mediterranean coast and that is why I chose the coast of the Bay of Biscay. Also, it is easy to get to other parts of Europe via France or head over to Portugal. The cost of living is less than in other coastal cities.
Please realize it is not a "city" but what I'd call a town. There is one department store on the edge of town and most people shop at the local shops and stores rather than go there. Like a lot of Spain, it is a town where you walk. But I have found the bus system here to be incredibly reliable.
I chose to live very near the beach with a view of it and so I get a lot of the wind when we have a storm. Further away you will not experience as much but there are days when the wind and rain will slap the entire peninsula for a couple of hours.
Finally, please realize this is my first winter here so I can't give personal experience beyond that. But from what people tell me, this is fairly typical. I recommend you come and rent (as I am doing) before you commit. You might compare a city you know using Weatherspark to see how it compares to Santander. For example, Santander falls between Seattle and Valancia for the amount of "clear skies". During the winter months, Seattle is cloudy 70% of the time, Santander is cloudy 60%, and Valencia 40%. During July and August, Seattle and Santander tends to be cloudy 30% of days and Valencia is cloudy 10-15% of days.
Personally I was concerned about it being too cold for me as I was born and raised in Alabama, lived most of my working life in southern California, and lived six years in Mexico before moving here. I like temperate weather and have never lived in freezing temperatures or where it snows. But Mexico was too hot for me. Santander is not too cold and I went to Paris last December in near freezing temps and was fine with my coat. I am surprised that in Santander a few days of it not being above 7 C (45 F) hasn't bothered me as I know it will return soon to the typical 10-13 C (50 - 55 F). I know that April will bring 16 C (60 F) degree weather and in the summer if it gets above 25 C (77 F), it will not be for long. I had planed to go to Valencia for part of January and February but chose not to do that as I was enjoying being here.
I'll paste a few pics with focus on the sky so you can see what days can be like here.
https://photos.app.goo.gl/WPGqV9cc1KvHMi989
https://photos.app.goo.gl/EAC9Mk8JVuqrbfPh9
https://photos.app.goo.gl/Ly8Ja8fgYXm9hZWPA
https://photos.app.goo.gl/16TVtYvdqadCB2Ai9