Coming in late here...
Regarding Madrid, we were there the fall before last, during the week, and found a fair amount of galleries closed. During the winter, there may be even more of them closed so your visit may be a short one.
While a bit out of the way, I would recommend a look at Santuario de Chimayo en route to Los Alamos, While not the least bit 'religious', I have a thing for old New Mexican churches, be they adobe or just interesting. This is a pilgrimage shrine, and the separate Chapel of the Holy Child of Atocha is sweet, with many, many pairs of little children's shoes given for the Holy Child's travels. Anyway, lots of traditional folk-art santos - both retablos and bultos - here: devotional images that figure into part of the colorful New Mexican culture. I'm including a nice PBS film about the art form:
https://www.holychimayo.us/chimayo
https://www.holychimayo.us/santo-nino-chapel
https://www.newmexicopbs.org/productions/colores/devoted-to-the-saints-new-mexicos-santos/
Lunch: Rancho de Chimayo. Check the hours closer to your trip:
http://www.ranchodechimayo.com
Along the way: very large Sacred Heart/Sagrado Corazón de Jesus adobe church in Nambé (on HWY 503). While we've never found it open, it's plenty photogenic, and the adjoining cemetery is a cheerful, interesting clutter of mementos; look for the burial monument that's a miniature replica of the church.
https://www.alamy.com/stock-photo/church-at-nambe.html?sortBy=relevant
https://www.loc.gov/item/2020742600/
https://www.nmmarketplace.com/articles/churches-on-the-high-road/article_dc19d542-c417-11e7-901f-cf0077647072.html
Speaking of folk art, yes, the Museum of Internation Folk Art in Santa Fe is a gotta-do: the largest collection of its type in the world. As well on Museum Hill, the Museum of Indian Arts and Culture is also top of list: "Here, Now and Always" exhibit is very good. Heck, all 4 of the hill's museums are well worth the visit. As well, visit the Palace of the Governors/New Mexico History Museum on the plaza.
Canyon Road: just walk and pop in and out of what draws your eyes...which will be a LOT! Near the far east end of the road is Cristo Rey Catholic church: one of the largest adobe churches in the world. WHY it's so big involves an amusing story around its enormous stone reredos:
https://www.santafe.org/listing/cristo-rey-church/330/
Other don't-miss S.F. churches are the cathedral, of course, Santuario de Guadalupe and San Miguel.
https://sanmiguelchapel.org
https://www.santafe.org/blog/post/guadalupe/
In for an uphill walk through history? This path zigzags up to (controversial) Cross of the Martyrs and a bit onwards the top of a hill overlooking the city: a popular spot for taking in sunsets (we usually stay nearby). This was once the location of Fort Marcy (1846). Along the way are timeline plaques outlining the long history of this oldest capital city in the US. The walk starts on Paseo de Peralta, just east of Otero St. Interested only in sunset? Drive up to Cross of the Martyrs parking lot in Prince Park, just off Kearney/Prince Aves. Reference a SF map and it'll all make sense. :O)
Why I said that the cross is understandably a controversial monument for the indigenous communities involves the Pueblo Revolt: "the only successful Native uprising against a colonizing power in the history of North America." This is a really important piece of NM history so well worth taking the time to read up on if you haven't already. Here's a good start:
https://santafelibrary.org/wp-content/uploads/sites/18/2022/04/Cross-of-the-Martyrs.pdf
Del Charro at Inn of the Governors is our favorite kick-back watering hole. Margaritas come in a generous shaker, and the food is inexpensive, non-fussy and good, or has been for us, anyway. Fave order? NM Green Chile Chicken Chowder. Yum! https://delcharro.com