They are interchangeable.
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ozzourtiNgram Viewer shows that "all year round" (no article) has been gaining popularity since about 1920, and now is a little more common than "all the year round". Both are in use, but I prefer the former.Interesting graph.
Blue JayAll year round is much more common.Edit: I didn't see ozzourti's post before I posted mine. I do think All year round is far more common, though.I think I have to agree. I usually say "all year round". The other version seems more formal to me for some reason.