Born and raised New Mexican here, NMSU grad (go Aggies!) Been in Boston the past 20+ years with a seven month stint in ABQ about a decade ago. Go back every couple of years to visit family and friends.
First question: which hospital? Albuquerque has dismal public transportation. Plan accordingly. My commute in ABQ was as bad as in BOS in terms of traffic. You will need a car in NM. Or two.
Horses: of course. Horse properties are in the city (NE and SW) plus both south of the city and to the NW in Corrales. You'll have no problem finding horse properties. If you can afford Corrales that is where it is at for close to the city + horses.
Education: Albuquerque Academy is well regarded.
Culture: I work with a bunch of folks from Ontario and find their attitude similar to New Mexicans. You'll fit right in. Trust me. Bonus points you're not Texan or Californian.
Feel free to PM me if you have questions and I might be able to help, but you got this methinks. Worst case scenario you get a couple cool stories out of it and learn the concept of mañana.