The poem is told in First Point of View.
How, and why?
"Ah, distinctly I remember it was in the bleak December;-"
"Eagerly I wished the morrow;- vainly I had sought to borrow From my books surcease of sorrow-"
The fact that the poem uses " I and my" can give you a clear idea that the speaker is reffering to himself/herself. Therefore it is in first person point of view.