Big snows fell on Beijing.语法对吗

肯定不对呀
应该是The snow is heavy in Beijing或者It snows heaviy in Beijing

名词“雪”可数，但单复数都是snow。
a big snow
several snow
通常不用“雪”作主语
it had a big snow in beijin'.

我的建议是改成：
Heavy snow hits Beijing.
(hit更形象一些）

改成 heavy snowfall in Beijing. 不完整句子

There is（was） a heavy snowfall in Beijing. 完整~

综合了一下，还是觉得三楼的比较好。Heavy snow hits Beijing.