When in the down I sink my head, Sleep, Death's twin-brother, times my breath; Sleep, Death's twin-brother, knows not Death, Nor can I dream of thee as dead:
I walk as ere I walk'd forlorn, When all our path was fresh with dew, And all the bugle breezes blew Reveill´e to the breaking morn.
But what is this? I turn about, I find a trouble in thine eye, Which makes me sad I know not why, Nor can my dream resolve the doubt:
But ere the lark hath left the lea I wake, and I discern the truth; It is the trouble of my youth That foolish sleep transfers to thee.
When Tennyson sleeps, he can forget. Notice how he equates sleep and death here. They are "twin-brother[s]," so when Tennyson sleeps it's kind of like death. He doesn't know Arthur is gone. During these times, what he doesn't know literally won't hurt him.
He dreams of walking with Arthur way back when, when they were first starting their friendship. Tennyson emphasizes this with images relating to beginnings: "fresh with dew," "Reveill'e" (which is the bugle song played to wake people up in the morning), and the dawning of a new morning.
In this dream, he notices that Arthur is sad, and this in turn makes him sad.
When he wakes, though, he realizes that it was just his own sadness that he was transferring onto the dream-Arthur.