The poem is important to Walton as it seems to have inspired his own love of exploration in far-flung regions. The poem is of course set in the polar wastes, and that is where Walton has ended up too. He is pursuing the romance, the challenge of a voyage to these perilous lands.
Walton directly invokes the poem, and its chief character the Ancient Mariner, in one of his letters to his sister.
I am going to unexplored regions, to "the land of mist and snow"; but I shall kill no albatross, therefore do not be alarmed for my safety, or if I should come back to you as worn and woeful as the "Ancient Mariner." You will smile at my allusion but I will disclose a secret. I have often attributed my attachment to, my passionate enthusiasm for, the dangerous mysteries of ocean, to that production of the most imaginative of modern poets. (Letter II)
Here, Walton admits frankly that the poem has inspired him in his choice of career, his pursuit of glorious adventure in these wild lands. He also remarks here that he will not be quite as willful as the Mariner, who was punished for gratuitously shooting an albatross; he declares he will not do the same, but he admits that he too might return as forlorn as the Mariner did. He is aware of the risks he faces, but at this stage he also comes across as over-eager in his bid for high personal achievement. He is getting carried away by his enthusiasm.
Later, Frankenstein also invokes the Ancient Mariner. The darkly romantic aura of that famous poem colours the entire novel, and also has a admonitory purpose. Just as the Mariner thought he could do as he pleased, and challenge nature itself, and was punished for his presumption, both Frankenstein and Walton are similarly over-ambitious; and Frankenstein too pays the price. It is left to him, while dying, to warn Walton of the dangers of over-reaching.