I think this is unanswerable, because there's no way to quantify appreciation.
I suspect the authors of the other answers have valid points when they point out that translations crippled by the requirements of scansion will often not be as good as the original text, but I'm fairly sure that there are exceptions. Scansion notwithstanding, some non-English idioms are pretty much impossible to translate into English with any degree of poetry (Così fan tutte, for example). But I'm not convinced that more and deeper knowledge always adds to enjoyment, and certainly not to a sufficient extent to justify the pain of its acquisition.
Take Shakespeare. I'm a native English speaker, and a fairly literate one at that, and I love Henry V; but I was really surprised to learn from Bill Bryson that some of the heavily-accented pseudo-English words spoken by Catherine in Act 3, scene 4 would have been gross (and hugely comical) obscenities to an Elizabethan/Jacobean audience. Is my appreciation less than theirs, because that passes me by? I don't know (though I'd wager that watching it without that knowledge but also without toothache, kidney stones, bladder stone, or lice, and with an actual woman playing Catherine, I have the better deal).
My point, such as it is, is that you can overthink this. If you can love Winterreise as a piece of music with accompanying random vocal sounds, do so. If you feel you need to know what the vocal sounds mean in order to appreciate it better, by all means follow a translation as you listen, or listen to a decent English version (I don't know of one, but then I also really don't like Schubert's music). If you feel you must learn German, then by all means do so. But don't spend your life feeling you're being cheated because at any given time you can only like a thing that you like in the way that you can, at that time, like it.