The poem "Full Moon and Little Frieda" is told in the second person point-of-view, which is the least popular viewpoint used in writing.
The poet uses the word "you" twice, speaking directly to the subject of the poem (Frieda).
I believe one reason the poet writes in this "person" is because it is an unusual form, and it is likely to grab the attention of the reader.
The second reason I believe he uses this person is because it is important to the narrator to paint a picture for the child that she will not remember when she is older, unless he takes a "snapshot" with words of the moment right now.
Note the following segment of the poem:
'Moon!' you cry suddenly, 'Moon! Moon!'
The moon has stepped back like an artist gazing amazed at a work
That points at him amazed.
(This is like the famous picture by M.C. Escher, called "Drawing Hands." If you have seen it, you realize the trick the picture plays of two hands drawing each other—you cannot tell which started first, or "who" is really drawing "who.")
Second person point-of-view draws specific attention to the child. Through the tone and the imagery used, we learn that the author's choice to speak directly to Frieda stems from his fascination with her: he is amazed by her—as amazed as she is by the moon, and the moon (through the use of personification), by her.
(In case you did not know, Ted Hughes was Frieda's father.)