First of all, I am not good at English but I have to mention this. İt's annoying me. Please excuse my usage of language.
''It is nice to see you.''
What is the subject of this sentence? What is the thing that is nice? Obviously, it is ''to see''. To see you is nice. But according to the sentence above ''it'' is subject of this sentence. But according to the reasoning, to see is the subject, too. In the final analysis, we can say that we have two words that have the same meaning. As long as two things have the same meaning we can use the one instead of the other one. Therefore, if ''it'' is the same thing with ''to see'' then we can say that to see is nice to see you.
Or let me ask you this: Why do you use such a structure? And what do you think about it?