The FEI issued a manual to support event organizers to make their event more sustainable. You can find the manual here: http://thesustainablehorse.com/fei-launches-sustainability-handbook-for-equestrian-events/
On a country level I see different levels of activity, where Sweden is the most active. http://thesustainablehorse.com/swedish-national-equestrian-centre-stromsholm-sets-example-with-iso14001-certification/
France did a good job with the Equures label, introduced in the WEG2014: http://thesustainablehorse.com/equures-horse-industrys-commitment-sustainability/. Not sure what the current status of the Equures label is, but that would be interesting to find out!
The European championships 2017 in Goteborg will be the first really sustainable equestrian event!