There is a huge history to dressage, it evolved out of old style cavalry show moves - the so-called 'haut ecole' - all based on the natural movements that wild stallions would show in intimidating/fighting other stallions or impressing mares. Even an 'average' domestic horse may still show some of these movements while playing loose in a field although not to the same extent e.g. my own mares will show a lovely 'passage' when begging to be first in from the field for their dinners 
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But obviously it isn't 'natural' for a horse to carry a rider and in order to get a horse to grand prix/international standards it is a long process of building their muscles and teaching them the movement to enable them to perform to that standard. These horses will start at the age of 3 or 4 and won't reach the Olympic level before the age of 9-10 at the earliest, and will probably only be able to keep going before their joints/muscles start to lose performance for 5-7 years. So not dissimilar to ballet dancers or gymnasts in humans. There are some welfare issues in modern dressage with horses being pushed too far too young or restrictive/cruel training methods but it is highly regulared now in international competition.
Do the horses enjoy it? On the whole I would say so although it is 'work' to them, you have to remember these horses are selectively bred over multiple generations to do this job and the ones you see that make it to the Olympics are the very small % that have both the physical ability and willingness/desire to consistently perform at the very highest level, the vast majority will not reach this level and will end up in a less competitive home, doing some lower level dressage and maybe also other activities like jumping, hacking alongside. Are the unsuccessful horses that do a more relaxed job maybe 'happier' than the elite athletes, possibly, I think similar could maybe be said for human sportspeople?? Certainly I can say though that horses are large willful animals, if one day one of these horses said 'enough, no more dressage for me' (as sometimes they do!) they could very much refuse to do it and it would be impossible to force them, willingness is an incredibly important part for any sports horse (whether showjumping, eventing, racing) and if they don't want to do it, they don't!