According to Wikipedia (which has a long summary of consonant variants in different dialects of English), pairs like "whine/wine", "whale/wail", and "which/witch" are pronounced as homonyms (i.e., they've merged to "w") in nearly all standard dialects of English worldwide. The exceptions are in Scotland, Ireland, and parts of the southeast US:
In these areas, people still say h'wine, h'wale, h'wich, and so forth. But in other regions, such pronunciations may sound old-fashioned or affected, so I would advise not learning it. (Honestly, h'wich and h'wine, etc., all sound ridiculously pompous to my ears -- it's an accent I associate with the stereotypical criminal super-geniuses from Hollywood movies. I don't remember h'wether Dr. Evil from the Austin Powers films actually had this accent, but I would expect he did, because that's h'wat tells the audience that he's evil.)))) In other words, saying "whine" as h'wine now sounds "hyper-correct" to most English speakers.
PS. If you check out the Wiki article above, I would also point you to the section on "Yod-dropping" -- this refers to whether such words as "do" and "dew" are pronounced alike, and whether the word "new" sounds the same as the second syllable in "menu," etc. Again, it depends on which dialect of English you're talking about -- I say "do" and "dew" identically, but people in some parts of the US South pronounce the two words differently.
You might also be interested in the section on "L-dropping", which discusses whether the L is clearly pronounced in words such as "golf" and "walk". Yet again, it's a matter of regional dialect.
I mention these three sections specifically because they talk about pronunciation differences that can be heard in certain varieties of "acceptable educated English." Some of the other phenomena are not accepted as "the educated standard " in any part of the English-speaking world -- so they're probably of less interest to a non-native learner.