PEACHY
(peach with pink mane and tail, hearts symbol)
Twinkles
TWINKLES THE CAT
(orange cat with black stripes)
Peachy's Parlour
In the UK at least, this seems to be *the* number one on the common pony playset list, and its hostess, Peachy (shown above with Flat Feet but available in concave hoof style also) is fairly common on the second hand market also. Sold worldwide, the playset was called the 'Grooming Parlour' in the UK and the 'Pretty Parlor' in the USA. However the only difference between the playsets appears to be the label on the end carrying the name of the building.
Peachy's stall like parlour came with a variety of simple styling accessories (well, it was only 1983, Hasbro had not got into major gimmick mode yet!) including brushes, ribbons, riding tack and hats. The parlour also came with it's own little 'friend' for Peachy - Twinkles the Cat (above).
Thanks to Garej for the use of the below Argos catalogue image of the Grooming Parlour.
 

THE GROOMING PARLOUR