So, with WWHD coming out, and OoT3D known to be an influence, I think it's likely we'll see WWHD get a new stage or character. Who or what might these additions be? What would be the best new things to include from WW?
I doubt we'll get a "new" character to be honest, we got Toon Link in Brawl, and I doubt they'd put a new character in, if they do, who? - would be the question. I don't think there is a character important enough to be included in the roster, I think they might go with a character from the newest installment, Skyward Sword.
However, I'd bet on them including a new stage or maybe a new trophy from the game, just to acknowledge it's release. Of course, we already got the the Great Sea stage in Brawl, so I think another one won't hurt. I'd like to see a stage set within the Forsaken Fortress to be perfectly honest.
If you ask me, the remake probably won't affect the new Super Smash Brothers any more than the original version of the The Wind Waker affected Brawl. My guess would be that, at the very least, they'd keep Toon Link from Brawl. Perhaps they might keep the Pirate Ship stage as a throw-back stage, similar to Melee stages in the previous SSB installment. I guess they could add another stage based on the game, perhaps an important island. In any case, I'm certain that there will be some representation, just not anymore than what was present in the latest Smash installment.
I expect minimal influence; a mere trophy or two in TWWHD's honor. The game really isn't groundbreaking from a pre-release point of view, but time will tell if it shifts Wii Us or not. Since we're waiting, I really don't think Sakurai or any of the other folks have any specific plans for any TWWHD content in Smash 4.
Not substantially so. Definitely not to the extent of Skyward Sword, or even Twilight Princess. A great number of the Zelda trophies will be based off SS, just as Brawl had all the TP and TWW character trophies. A (new) Wind Waker stage is entirely possible, just as Ocarina of Time has a new stage, Gerudo Valley, in the 3DS title due to its remake.
In terms of new characters, I don't see anything possible. Some seem to desire a Toon Zelda with Toon Shiek/Tetra for whatever reason. I expect the main trio of Zelda characters to use new models heavily based off Twilight Princess, like we've seen for Link so far. Toon Link may use his TWWHD model, I guess.