Zelda is definitely not "too" happy. It bears a happier, more lighthearted edge than a lot of other franchises, yes, but it's not sunshine and giggles all around. It's more about the light pushing through the darkness than the darkness itself; it encourages players to find their own inner heroes and be brave, which is part of why Link's status as a connection to the player is so important.
I think in general, Zelda should pull a lot of its story inspiration from Fire Emblem. FE is not really a "dark" series, but neither is it notably happy and lighthearted. Zelda is much the same way, but the difference is in story execution. Fire Emblem gives you frequent humor, sometimes stereotypical but oh-so-enjoyable characters, and shies away from the "harsh" end of the spectrum (for instance, in Radiant Dawn, Almedha is implied to be Ashnard's concubine, but it never goes much deeper than this). At the same time, it isn't afraid to show you character death, ugly betrayal, and implications of things like torture and sex. It's not a "dark" series, but neither is it considered "light." It has an excellent balance of the two, and it usually has a deep, emotional, interesting plot with few to no plot holes.
Zelda needs to be the same. It needs to retain its general balance of light-to-dark, but flesh the plot out so it's deep, emotional, and interesting with few to no plot holes. It really hasn't done this so far, even if its stories have been fun, so I say take a leaf out of Fire Emblem's book.