How does 还 function in 快下雪了，我还以为今天是好天气?
It implies that I had been thinking today is a good day, until I noticed that it would snow soon. 还 means 本来 here, it indicates a continuation of original thought. For no. 3, I wouldn't say it's wrong, but it sounds very Chinglish to me. 

It couldn't be "also", because 快下雪 means bad weather, which is opposite to good weather.