Looks like the choices are in-room tubs or public tubs (some with private remtal times.) Do any have outdoor tubs on a private patio?
To add to the previous reply: Riverbend Hot Springs has both public and private outdoor tubs, all with a view of the Rio Grande River. Read all about it here:
Sierra Grande also has some outside, private tubs. We've always enjoyed ourselves there, whether inside or out.
As does the Charles ... Rent one of the two second story rooms and get all night access to a private tub ... carracar
La Paloma Hot Springs has private outdoor pool called LongHouse in Truth or Consequences