Madrid in mid-January

Layering is the way to go. It is chilly at night

Thanks, J+T. We are used to layering, and since we probably won't be back to the hotel as it transitions from day to night, I didn't really want to lug a heavy coat around during the day.

Madrid sits on a high plateau. May be the highest European capitol with regard to elevation. When we were visited our son in March during his spring break we actually encountered snow. Granted it was light and didn't accumulate but it was 30 degrees day that day. So dress in layers. It can get chilly. I always used a wind breaker/rain jacket, down vest, sweater and long sleeve undershirt plus a hat. When it is chilly a hat is almost more important than a heavy jacket.

https://www.worldweatheronline.com/madrid-weather-history/madrid/es.aspx

There are many other such weather tracking sites.

When I was there in October a couple of years ago, it was cold and windy.
People there told me it is quite cold in the winter months, as it is apparently the highest city in altitude in Spain.
So, I think if you take many layers and some good warm boots, you'll be fine.
Lots to see indoors if need be!

I have been in Madrid a couple times in February, probably more late February, and it was moderate during the day, not warm, but not cold. A light jacket was plenty. Weather tends to be drier.

My usual plan of a light rain shell (Marmot Goretex shell); a fleece type jacket, then a backup of a sweater or heavy shirt worked well.

I was there in January; you do not need boots in Madrid just wear some socks and shoes with a firm sole

Thanks for the input, everyone!