The model on the left was purchased as part of the Target #720230 Pony Gals - Country Vet Play Set (2009) while the one on e the right was purchased as part of the #5927 Down on the Farm Play Set (2009-10). The model was also used in #710724 Emergency Animal Rescue Set (2009-15) which was sold through various retailers.
Colour, shading, and finish can vary a bit, but the model is a mousy brown with a hint of grey, with lighter belly shading, some light shading on the face, darker hooves, and sometimes faint dorsal striping, muzzle and mane/tail shading.
#701720 Stablemates Visiting Vet Horse and Trailer (2012-14) might be extra #5927 models, but some collectors have reported that these models are lighter and more grey-brown than brown-grey.
The grey models are slightly easier to tell apart, thankfully.
#059204 Stablemate Deluxe Animal Hospital (2010-Current) is a matte medium grey with white shading on the belly, legs, and face. The mane/tail, hooves, muzzle, and forehead are darker. This model was also released as part of the JCPenney Stablemates Animal Care Center (2010)
I haven't been able to decide if (top-right) #5366 Ranch Friends Play Set (2013-14) and (bottom-left) #5950 Petting Zoo Play Set (2012-2013) are identical releases or not. Both are a pearly white-grey with slightly darker mane/tails. My #5366 is a slightly warmer grey with a touch of pink shading on the nose and a little dark shading on the legs. My #5950 is a more uniform cool grey with shaded hooves.
The model on the bottom-right is a #5950, but is darker than his sibling and has leg shading like #5366. He looks like he could be a variation from either set, but I marked him when I opened him so I'd remember which one he came from. He's also a bit of a factory "oops" as his front hooves and tail weren't molded properly.
Many thanks to Amanda Reed of PixelPerfectStables for providing pictures for this post!