两词所表示的范围不一样，go skating表示去滑雪、去滑冰，go skiing只表示去滑雪。

go skating释义：

去滑冰；去溜冰

例句：

It was so cold that we were able to go skating on the lake.

天气极冷，我们能到湖上去滑冰了。

视频：

场景会话释义：

去滑冰；去溜冰

例句：

It was so cold that we were able to go skating on the lake.

天气极冷，我们能到湖上去滑冰了。

视频：

场景会话

go skiing释义：

去滑雪

例句：

We go skiing most weekends in winter.

我们在冬天的周末大多去滑雪。