Vela can probably answer more knowledgeably, but I do not think any horse naturally gaits that way (the big lick gait). From what I understand, weights and chains are usually used to train them to walk that way but not everyone uses soring. A great many do though, and find ways to hide it from inspections. Their natural gait is just nothing like the "big lick" gaiting.
Here is a little clip of a walker foal gaiting from birth. It seems natural with them the way retrieving is often innate in retrievers from birth.
http://www.youtube.com/watch?v=4HSkwF586ro
Racking I think is another type of gait a little different from flat-shod walkers but again that's not an area I'm as well educated in as Vela is.
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