"16-bit era pixel art" should be the google terms that will get you started. I don't think there's a more specific style than "Pixel Art" that will help you out much.

EDIT: Attached image from wiki for reference:

[attachment=13284:Legend_of_Zelda_a_Link_to_the_Past_Screen02.png]

Your question goes more towards art direction, as has been pointed out.

The kind of "view" they used would most-typically be called a 3/4ths overhead perspective, but its worth pointing out that they also do it in a slightly different way than most games, which is that the backside of some structures is visible--but is "shorter" than the frontside of the same structures. For example, in the screenshots that Prinz Eugn posted, you'll notice that the backside riverbank near link is visible, and that its a single tile high, and so are the side-facing riverbanks--but viewed from the frontside, the riverbank of the same structure is about twice as high. Its a kind of faux-perspective that really only the Zelda series does, its also functional as it facilitates the ability for link to jump down to lower levels and for the view to remain unobscured.

I'd personally classify it as a chibi or SD art style, but that's not any kind of official classification.

I'd personally classify it as a chibi or SD art style, but that's not any kind of official classification.