It may look like their sniffing the ground but really what their doing is submitting to you, and telling you that you are the alfa.
Its kinda like a dog rolling on its back so you can pet it, haha.
. I think that this body language may often be submissive, but it may be just sniffing. Whether it's submissive or not, the horse telling you that you're 'the boss' or not, I also don't think that it necessarily denotes 'respect', as especially with 'round pen' type exercises, the horse may be doing this out of fear/hopelessness. I think it's important to understand all
the bodylanguage that is going on, as taking one signal like that may lead you to the wrong conclusion.
I don't think it's appropriate to compare equine behaviour to dog behaviour, especially when talking about 'dominance' & 'submission'. Also there is so much unfounded speculation about dog/wolf/human behaviour in this regard, and I think the above is another example of something that ain't necessarily so, and isn't necessarily very helpful. For eg. a dog may well roll on it's back to demonstrate submission when it's afraid. It may also roll on it's back confidently & get a belly rub. It may also roll on it's back to instigate
a belly rub, because it knows this behaviour causes you to give it a rub - that is, the dog is in control of the situation, is demanding attention.
Generally speaking, I don't really buy into the dominance theory much, for either species. I'm quite comfortable with the dog/horse feeling in control of the situation, so long as it doesn't interfere with the desirable behaviour I want. For eg. if the horse thinks he's training me to give him scratchies, treats, whatever, and cueing me with 'polite' behaviour, that's fine by me. I think trust & *mutual* respectful behaviour is important, and I think it's also vital(for safety if nothing else) that you can be the leader in the partnership when necessary, but I think this is completely different to the dominance/submission concept.