Even with the 'statement' that Termina is "a kind of parallel world that is similar and yet different from the land of Hyrule," I feel it's possible to still argue that the entire thing is just a dream conjured up by Link.
He does take a pretty nasty fall from his horse right at the start. The only inconsistency up to that point is that...he's riding a horse as a kid. We can't forget the "rabbit hole" part of the opening where Link falls down...a hole...seeing some strange things on the way down. A child-like fantasy of being 'Link in wonderland'.
Barring that, he can now wield a metal shield as though he was older.
OoT he couldn't use the hyrule shield properly like he can in
MM. Admittedly, this might be a weak point as the
MM shield seems like a smaller version of it. Then there's the archery. Young link couldn't wield a bow in
OoT. I know Links in other zelda games could, of course, but they could do a lot of things that other Links couldn't.
Then, of course, there's the characters. The mask salesman could very easily represent a type of "mad hatter" clearly being out of his mind. And, while yes, the re-using of characters is more than likely (most definitely) chalked up to cutting production time, there's no real reason why they couldn't have used this as a story aspect as well. Taking into consideration the dream theory, and the fall from Epona, I could (and am going to) argue that another aspect to the dream is that everything i jumbled up inside of Link's head. The gorons are frozen, instead of the zoras for example (it would also explain that horribly deformed Goron Chieftain). The twin witches boss from
OoT are just npcs, etc. Some npcs are repurposed, while others are not, like the mailman. I don't really see how this is a counterpoint to the theory that it is in fact, a dream.
MM is also the only game that has aliens (as far as I can recall). No, we could not possibly relate that to simply being the inner workings of a child's fantasies. I mean, they're stealing cows...
Returning to the 'Link in Wonderland' thoughts, there's a few others aspects that hint toward this. For example, being able to become giant, putting the deku princess in a tiny bottle, the owl (cheshire cat?), the deku castle (queen's castle) plus deku patrols (card knights).
I could go on but, I should relent, to see if anyone has some counterpoints (or if anyone is going to bother responding at all, I know this thread is kind of old/not actively followed).