Hi there!
Madrid is mostly informal as far as coats go. Regular parkas are acceptable even over a suit, although the "pijos" or Spanish yuppies tend to have an expensive brand, mainly "Barbour" which charges 400$ for a wind breaker!
Also, many women wear long down coat as that was last year's trend. Long wool coats for women tend to be only if going out to a nice dinner, theatre, etc. Any mid-length coat, wool or otherwise plus gloves and a skarf (hats are rare, in general) should do perfectly.
Enjoy your trip!