One must be careful about this rule: It applies to words beginning with vowels, etc. Thus, even if a masculine noun begins with a vowel, if it is preceded by an adjective which begins with, say, an n, then you'd use il instead of lo.
lo stivale but il nuovo stivale.
The presence of mio thus removes the necessity of using lo, and nel mio stivale would be correct, grammatically, as it is actually in il mio stivale.
But then, as MadelynWrit points out, you don't need mio - but then without the mio you have to use nello, so it's either:
nel mio stivale or nello stivale
but that doesn't answer why it would not be "ON the boot" compared to "IN the boot" because you can have things on your shoes that are not inside your shoes. Sometimes I have mud or a bug ON my shoes but not IN my shoes (thank god). Semantically, could both IN and ON have been correct in this boot case? If not, how would you say "I have a snake ON my boot" ?
When you're learning a foreign language, you just have to accept that prepositions won't make much sense to you in the other language. They don't translate well if you're just trying to find one equivalent word. Instead, you always have to think of them as part of a phrase and memorize them that way.
two good and easy charts for prepositions
I've been collecting e words in a list of feminine or masculine. Here's what I've collected so far:
prigione prison, jail
costume costume, suit, bathing suit
dolce dessert, sweet
The difference between and nello and nel is the same as la/il and lo. Use the one that ends in o for words that start with s+consonant and z+consonant. Il piatto would be nel piatto. Lo zucchero would be nello zucchero. Etc. It took me a little bit to realize that as well because it isn't very well explained, but if you know which "the" to use then you'll also know which "in the" and "on the" to use.
These are called "prepositional articles" because they combine a preposition and and article together. There is a nice chart showing the different forms at http://italian.about.com/library/fare/blfare153a.htm
Partly because "nello" means "in the" and not just "in". So you at least need the "the" to make a coherent English sentence. But as a previous commentor said, the "my" is implied because Italian doesn't use possessives for clothing unless you're specifying whose item it is. If there is no possessive it is accepted that you're talking about your own item.
So, can it be "Io ho un serpente nel mio stivale," if you're trying to be completely clear?
I only started Italian a few months ago and I am finding the lack of personal pronouns and possessives difficult to grasp. This I translated as ...in the boot, which was accepted. The implication was that it was the speaker's boot, but I have found Duo gets a bit touchy if you put in words that are not actually there.