Should I write go down into the valley or down into the valley?

In the first, it could be construed as following the path with your eyes.

In the second, you followed the footpath across the field which led you down into the valley.

What you should write depends on the actual surroundings in which you place the action and the action itself; from the second sentence it is clear that the action considered includes going down the valley and so we can presume that in the first sentence this action is understated since you are considering either sentence to relate to the same action; if the footpath has a continuation out of the field and into the valley then it doesn't matter which you write as far as meaning goes; you remain true to the facts. However, if the footpath stops at the end of the field and it is necessary so as to continue towards the valley from that point on, for instance, to do some climbing down of rocks , then you can't use the first one since that first one implies the same footpath leads down into the valley.

The reason for that is that you have to consider "the footpath across the field and down into the valley" as a noun phrase in which are found two prepositional complements linked by the conjuction of coordination "and": the noun phrase can be paraphrased as "the footpath that went across the field and (then) that went down into the valley".