"You're right that the conclusion only follows if the premises are true, that's why "dogs have wings" isn't a valid conclusion, like you said, since the premises are false."
Be careful now. You're still conflating "valid" with "true". These are two separate concepts. Truth concerns accurate descriptions of reality. Validity is a form of logic. An argument is considered valid if its conclusion follows logically from its premises, regardless of the truth value of any of its statements. That's where the logic comes in - that if you presuppose this and that premise, it implies a particular conclusion. You can only presume that a conclusion is true if both its premises are true, and the argument is valid - meaning, that it is consistent with the rules of logic. (And that's a longer lesson).
Anyway, I very much appreciate your patience and willingness to learn.