I'm not an expert on Italian, but I know that in French and Spanish - two other Romance languages - you generally don't use possession to refer to clothing. Same with body parts. They tend to refer to them much more... absently than English-speakers do.
It's implied, I guess. You couldn't say (at least it doesn't sound right to me) "I have a snake in the boot" in English, but in Italian, I even think it's the natural thing to say. That's how it is in my language, which is Romanic also.
I think it would be "nel mio stivale" (not "nello mio stivale", as you wrote). Because you have to pay attention to what comes after the member (la, il, lo) or the preposition (like in). Just like it's l'amica, but "LA mia amica" (not l'mia amica).