At first, it seems like the image of soldiers is just one more instance of Graves saying that children experience things differently than adults. But in reality, these soldiers introduce a whole dimension of adult life that struck very deep at the core of Graves' personal experience. Graves himself was a soldier in World War One, and the experience of fighting left him traumatized and fragile. In fact, the only way he could recover from the horrors of WWI was to talk about his experiences and to make sense of them by putting them into words. As you can probably imagine, this experience is reflected in the ideas Graves expresses in "The Cool Web."
When he first mentions "the tall soldiers drumming by" (4), Graves suggests that children don't really understand all of the significance that's attached to the soldiers. The children don't understand the horrors of war or the complicated historical reasons why countries go to war in the first place. But Graves is also implying here that the reality of war is something that adults constantly have to come to terms with, and that adults can only do this by putting their opinions and experiences into words—hey, kind of like Graves is doing by writing this poem.
Line 4: When the soldiers first pop up in this poem, they seem like they're just another example of something children don't have the ability to talk about. In this sense, the soldiers are "dreadful," but no more dreadful than the hot day or "the scent of the summer rose" (2).
Line 8: Graves has mentioned the "dreadful soldiers" once already by mentioning how kids don't know how to make sense of them. But here, he talks about "our" relationship to the soldiers and says that, through language, we're able to "spell away the soldiers and the fright" (8). In other words, we can think of scary soldiers and make sense of their existence through words, reminding ourselves that war has always been a part of history and that the soldiers are there to protect us.
Lines 17-18: By this point in the poem, Graves has suggested that language might be a bad thing, since it tends to dull our experience of the world. But in the final lines of the poem, he says that if we didn't have language to help us rationalize our lives, we'd have to face "the dark sky and the [war] drums" (17) directly, and we'd probably "go mad no doubt and die that way" (18). In other words, he's saying that our experiences would be way too horrifying and overwhelming if we didn't have a way of filtering them out. Just imagine if you suddenly got it with all of the horrors and suffering that are going on in the world. You'd probably go totally crazy. In the words of T.S. Eliot, "humankind cannot bear very much reality," so we need language to help us filter it.