I'd love more ambiance with weather. For example, if on a windy day, the trees would move around in the wind. I'd also like to see storms/blizzards that keep animals inside (as has been said previously). Having blizzards during the winter and tropical storms during the summer would be interesting.
Other ideas people have said here are also great. Fog/dew/frost in the morning depending on the seasons and so are puddles after rainstorms.
I know they have the weather channel on the TVs, but I'd love an actual weather report. Maybe, instead of an instrument shed, there was a screen or board that showed the weather for the next 7 days. And, as the days got closer, the weather could become more accurate of what actually would come. So, that way, you could always refer to it to see upcoming weather.
Another unique feature that I would like would be villagers commenting on possible tropical storms (or hurricanes I guess, but they wouldn't do any real damage except for maybe taking down trees) or blizzards that could reach the village. Have different personalities with different dialogue on this. For example, peppy villagers may act frightened, normal villagers may be practical and talk about stocking up supplies, and crankies may talk about how no weather is going to stop them.