In Game of Thrones, when Daenerys says "Khal Drogo has given me the wind", she is talking about the horse he gives her as a wedding present. Since, Khal Drogo's language has no word for "thank you", this is Dany's way of showing gratitude. "Given me the wind" in this case, is symbolic of Dany's horse. Some people compare riding a horse to "riding the wind". There is even a famous saying "Ride like the wind", meaning "ride really fast".
In conversational English, to "catch wind of" means that you have heard some information that was meant to be kept secret.
Q: "Did you know Anna is pregnant?"
A: "I caught wind of that in the conference room."
However, it would be incorrect to say "I have been given wind that Anna is pregnant." If you are speaking to someone, you would say "caught wind" because it is referring to information you learned in the past.
I hope this answers your question!