In conversational language, "All my hats..." implies that the speaker has at least two hats, which theoretically means that the sentence could be a lie from them having exactly one hat (even a green one). However, in practice, I don't think anyone would actually call that a lie. I think we treat the "I have hats" part not as part of the sentence itself, but more as an underlying premise.

You could have a similar situation in pure logic or math - if I were to say "the largest prime number is odd", is that false? Or something else entirely? (This is what Hofstadter calls mu, from a related concept in Zen.)