"Ranch" implies, if not denotes, work. If you are seeking a trained draft animal or a horse to herd cattle with, a ranch is the place you go. Horses are not intrinsically part of the definition, but are traditionally present. Thus, you would, if you were looking to get such a horse, specify "horse ranch".
If, on the other hand, you want a horse to race or tool about on, you hit up a trainer's stable. There are, as noted elsewhither herein, multiple sub-types of stables, but you don't need to specify further if those distinctions are not of interest. Similarly, it's accepted as a term for the entire complex and not just specifically the housing.
Re the dialects (Many USA) that I'm familiar with:
Neither "horse ranch" nor "stable" will seem quaint if used as described. "Stud farm" would only seem off if used for more than a breeding ground. "Horse farm" would be clearly understood, but would sound a bit childish, and would not be taken to imply anything other than a breeding facility.