That wouldn't work. Some people don't have WiFi connected to their Wii's.
Anyway, environmental conditions could work well. Just like the day/night cycle, some random rains and snow would be fine. Also, i'm sure if there is an ice based place, we'll have the snow stuff.
Well, depending on the season (EVERYONE will have that set up) the weather could change, like in autumn, it could rain and maybe have frost but not everyday.
Yeah, that would be awesome too! Imagine if it was thundering and lightning outside and you could see those effects in the game, that would be pretty cool. So yes, I agree that environmental conditions would make the game a lot more interesting.
Sorry to rain on your paraid (Bad pun, lol), but in the health and safety manual it says that you shouldn't play on the wii when there is a thunder storm, because if it is on anr lightning strikes your house, the wii could get damaged. But I believe that that would look awesome!!! It would make for epic battles in outside boss fights!
EDIT: @Meego7, Yeah! In the winter, if it's icy, then maybe blocks would slide more if pushed and in the summer, water could dry-up and that would make pools deeper and (assuming there is a water temple) then your job would be easy, unless it all freezes over, then you would have to bomb it to make a hole in the ice!!!