The speaker knows that it is the ice that made the tree limbs bend, but prefers other possibilities and/or metaphors:
But I was going to say when Truth broke in
With all her matter of fact about the ice storm,
I should prefer to have some boy bend them
Frost also compares the bent branches to girls' hair as they are bent over, drying their hair in the sun. Being bent over with their hair falling towards the ground (as the branches bend toward the ground) does suggest a bending to nature's or someone' will. This image of girls in a subdued or even submissive position, and sexual buzz words like "riding" and "stiffness," suggests a possible sexual metaphor; but this poem is more often interpreted as a metaphor for the imagination and nostalgia.
Note that the speaker "prefers" the idea of the boy swinging on the birches as opposed to the reality of the ice bringing the branches down. He prefers his imagination, the metaphor. When life is difficult, he prefers to imagine he is, nostalgically, like a boy swinging on birches. Through the imagination (and the metaphoric artistry of poetry itself), he can get away from daily life. Frost uses this idea of climbing the tree to illustrate how to "get away from the earth awhile." The imagining of the metaphor is a way to get away from daily life on earth; and the image itself, climbing the tree, is a literal illustration of getting away from daily life on earth, even moving towards another plane of existence: heaven.
Once he's had this mental escape, the branches bend back down, delivering back to his daily life. In this respect, the branches (birches) are the means of this escape, the means of imagination, because they take him (or the boy) away from the earth.
Frost compares the birches to "girls on hands and knees"