I love your hat.
I understand that there are several possibilities: suo - tuo - vostro.
But in what kind of situation have several persons one hat?
Even if they have the same hat(s), e.g. a group of soccer fans, it should be "I love your hats.
Or is it the old polite south Italian form? Then it is the first time I see it here.
The only plausible meaning, IMHO, is that “vostro” is used as a respectful singular you.
On the other hand, I think that “amo” in this case is not the best choice of words.
We do use “amare” for things we are fond of, but it feels a bit strange to use it for something that is not mine.
I’d go with “Mi piace il tuo cappello”, or if I were to give an over the top compliment “Adoro il tuo cappello”.
Edit: I just checked on tatoeba, and added my version.
The original sentence is in English, and a bunch of Italian translations have been added, with all possible permutations of “you”. Of course the clozemaster algorithm had to chose the least common variation! 
I read this as singular formal, perhaps to a stranger or an older person;-)
“Io amo i vostri cappelli” for many hats. Totally agree about “amo” - adoro would be much better or simply “mi piace”. Thanks Mike-lima.