1）这个说法是有的,一般出现在口语里,口语里的句子很多会让你匪夷所思的!
如：Why you?Why asking?等
2）例句的意思,相当于省略了主语you的句子：
即 Why don't (you)like winter in Beijing?
3）符合语法的正确的组为：
Why not do sth
=Why don't/didn't you do sth
=Why doesn't she/he do sth