First of all, as johann_ka explained, "music" is an uncountable noun. This means that if you are referring to "music" in plural, you still call it "music" instead of "musics" (and you would say "that music," not "those music"). Also, in your second sentence, you said "[that is music] from a completely different culture that of your country culture." This sentence doesn't grammatically fit together; I suggest saying something like "that is music from a completely different culture than that of your country's culture," because the word "than" compares the "different culture" and "your country's culture" (and the 's after country shows possession).
The sentence "How do you feel about this music?" is a question. You only use the word "do" like that in a question.
The sentence "I wonder how you feel about this music" is not question; it is as statement. You are not asking how the person feels about the music, you are simply saying that you wonder how they feel. Since it is not a question, you don't use the word "do."
Also, I don't know the purpose of your letter, but if you are trying to get a response from the person you are addressing the letter to, I would suggest using the question version "How do you feel about this music?" If this doesn't apply to your letter just ignore my suggestion.