I think outfit switches would be cool in a game, climate-appropriate outfits - and since we've moved beyond N64 in graphics, they don't have to be just color-coded. As stated, a nice warm (fur lined, perhaps) cloak for snowy-cold places and ice dungeons, perhaps something breezery or Bedouin-inspired for sandy, hot desert areas, a nice suit of armor for heavy combat/to mix it up...
However, I think these should come with stipulation. If you switch Link out of his tunic and light mail into his heavy armor, his movements become a bit slower - not iron-boots level, but just *a hair* slower in reaction, to simulate heaviness and how such armor would work in combat. It would protect him very well, but he'd have to sacrifice speed. (It could be sort of like your heavy fighers vs. fragile speeders on fighting games). Now, in special areas, such as an ice dungeon, perhaps wearing the regular garb instead of the winter cloak would have a PENALTY EFFECT - as in, there is a slow health-drain if you're wearing the non-cold appropriate wear (and perhaps, every once in a while, Link pauses to cough and sneeze to reflect his hypothermia). This would serve as a small penalty, but also as a gameplay variety device: Those people who enjoy a challenge might like to keep him in his standard tunic just to have that extra challenge to surmount. (Again, I'm thinking how in Soul Calibur II in one of the modes, how some stages will start out with your character poisoned and fighting against the clock on a slow drain of health).
I'm not in favor of Link getting a huge closet full of clothes, but a few weather and condition appropriate alternates in addition to the some of the things we've seen and some added necessity could bring some vareity to the gameplay.
Then, again, as said before, I'm also in favor of Link getting a green cowboy hat, blue jeans and a six-shooter on his hip - that is, if I and my fic co-writer are paid royalties.