I'm writing a business recommendation, and since it's a proxy for a proper name, it seems like capitalization might be in order, but it looks odd.
The only word that should be capitalized is the first one, "To", since it's the beginning of a sentence, even if it is a fragment on its own.
The only words that are capitalized on their own are proper nouns, and standing in for a name doesn't promote something to proper-noun status. Otherwise we'd have to capitalize pronouns ("I heard that He said to do this"), which is generally only done when referring to a deity.
An exception to all of this is when something is a title. Unless you're writing a book titled "To Whom It May Concern", in a letter, this should be capitalized like a sentence.
I see no particular reason to put the first letter of any of the words in capitals except the first one, but it's really a matter of personal style. You could capitalise all the initial letters, or you could put the whole thing in capitals and underline it if you thought doing so served some purpose.
(You might want to consider whether you need to use such a salutation at all.)