Some fans are warning they will boycott the Games's equestrian event - due to be held in South London - over what has been labelled 'the blue-tongue scandal'.
The British Horse Society has called for an urgent inquiry into the practices being used on some of the world's most expensive competition horses.
The controversy started when a video posted on YouTube showed a dressage horse being ridden using the 'rollkur' technique - also known as hyperflexion, the practice involves drawing a horse's neck round in a deep curve so its nose almost touches its chest.
Swedish jockey Patrik Kittel - who has since received death threats - can be seen warming up his horse, Watermill Scandic, at October's World Cup dressage qualifiers at Odense in Denmark using the position. The animal's tongue appears to loll out and turn blue.
The footage has angered tens of thousands of fans, who have signed online petitions and written to the sport's governing body Fédération Equestre Internationale (FEI), based in Switzerland.
Some are even threatening to boycott the 2012 Olympic equestrian event, which is expected to attract 23,000 spectators.
Lady Sylvia Loch, dressage trainer and author, told the Observer: 'It is a shocking symptom of where the sport is going, it's the tip of the iceberg. What is going on behind closed doors in the training of these horses is very wrong.
'Dressage should be about lightness, freedom of movement and a partnership between horse and rider.
'Rollkur is so, so cruel. The horse can only see its own feet, so it is reliant on the rider for balance which is simply psychological torture.
'Dressage should be a delightful ballet where the work looks effortless. It doesn't need vile and unnatural methods. Horses shouldn't be brainwashed like this.'
Patrick Print, chairman of the British Horse Society, has written a letter to the FEI, asking it to investigate.
He wrote: 'In our view, the concerns so widely expressed are reasonable and therefore deserving of an urgent two-part investigation.
'First, an inquiry into the treatment of this particular horse on this particular occasion; and, second, a broader inquiry into the ethics and consequences of hyperflexion.
'Please note that we pass no comment on the aesthetics of seeing a competition horse contorted in a way it never appears to choose for itself. Our concern is only to speak out when we believe that the welfare of horses demands it.'
But supporters of rollkur say it is a 'valuable training method' to improve the suppleness of a horse.
Roly Owers, of the World Horse Welfare charity, said: 'In the right hands it is a valuable training method, and it cannot make a horse's tongue go blue, no matter what people seem to think.
'Current rules do not allow prolonged or extensive use of rollkur. However, the incident has brought into focus that issues need to be ironed out.
'I wouldn't like a ban, as the method will simply be used albeit not in public. It will go underground.
'I don't think that people inside the sport realise the strength of feeling that is out there. There has been quite a phenomenal reaction to this, and clearly we want to see the Olympics bring more people into equestrian sports, not drive them away.'
A spokeswoman for the FEI said: 'FEI's main concern has always been, and will always be, the welfare of the horse.
'We are taking the issues raised in the video and in the comments made by members of the public very seriously and have opened a full investigation.'
But Kittel, the jockey at the centre of the controversy, claimed he 'did not ride Scandic in this depicted frame for the entire duration of the training as implied'.
He told Horse and Hound magazine: 'Scandic was a little hot at Odense, so I rode him for longer than usual. Throughout every training session, including this one, I give my horses walk breaks...
'Scandic sometimes plays with his tongue. During the filmed period of my training, he caught his tongue over or between the bits. I stopped when I noticed and put it back in the right place.'
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Swedish jockey Patrik Kittel has received death threats
Controversial: The rollkur technique involves drawing a horse's neck round in a deep curve so its nose almost touches its chest
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