Yes for sure! A good example is the Swedish Lovsta stables, home of the Olympian dressage rider Tinne Vilhelmson Silven.
This stable is ISO14001 certified and take sustainability into account in every purchase or decision they make.
Lovsta also organizes a competition series for young Grand Prix horses for which the compensate the CO2 emission for all riders and judges for the kilometers they make to go to and from the competitions.
Read more about this here: http://thesustainablehorse.com/swedish-lovsta-future-challenge-compensates-co2-emission/