its指the stream wound 引申为弯曲 wound its way 是以 the stream 为主语的动宾结构 为避免重复 使用its 代替
这是个常用搭配如 He is on his way home He made his way home.
一楼说的有道理。比如新概念三里有一个词组是find one's way to,也就是“某人去了某地”。还有make one's way to也是差不多的。