We first see ice in the letters of Robert Walton, who introduces the frame narrative through letters that he writes to his sister. Walton is on a journey to the North Pole in an effort to find a passage from the Pacific to the Atlantic. In this setting, we see ice emerging as a symbol of unexplored territory.

The primary plot follows, with Victor Frankenstein pushing scientific knowledge and boundaries to create a humanlike being via his own, independent work. Frankenstein explores realms of science that have never been touched and lives to regret doing so. He spends most of the book in conflict with the being he's created and offers no guidance or support to the creature. Completely isolated and desperate for companionship, the creature finally returns to his creator to argue that Frankenstein should create a companion for him. Note Frankenstein's inner dialogue:

A creature who could exist in the ice caves of the glaciers and hide himself from pursuit among the ridges of inaccessible precipices was a being possessing faculties it would be vain to cope with. After a long pause of reflection I concluded that the justice due both to him and my fellow creatures demanded of me that I should comply with his request. (Chapter 17)

As Frankenstein weighs this decision of returning to unexplored moral territory—What if the new creature is evil? What if he cannot control her? Is he making the situation better or worse?—the symbolism of ice reemerges.

Ultimately, Frankenstein begins this project and then destroys the creature's intended female companion right before the creature's eyes. Devastated, the creature vows to be with Frankenstein on his wedding night. Keeping his word, he kills Elizabeth and then disappears. Frankenstein searches for him, conveying the danger of the wandering creature to the local magistrate, who questions Frankenstein:

Who can follow an animal which can traverse the sea of ice and inhabit caves and dens where no man would venture to intrude? (Chapter 23)

The story Frankenstein tells is fantastical, and the magistrate must cross unexplored mental territory to determine whether these are the words of a rational or insane man—and how to best handle the situation if the words bear truth. He is presented with an almost impossible challenge of bringing to justice a creature which Frankenstein has portrayed as superhuman in strength and incredible in intellect. Therefore, an even more pressing concern is whether the evil which Frankenstein has unleashed on the world can possibly be stopped.

Through various plot developments, ice is used as a symbol to show the unexplored realms of human thought and science, which in turn contribute to the cold and nearly hopeless tone throughout much of Frankenstein's conflict.

Ice is commonly used as a reference to death because it is cold and life is insupportable there. It is also unchanging and hard while also being brittle, sharp, and desolate. These things are all symbolic of both Victor and his abomination—the creature of his creation.

When Frankenstein creates the creature, he brings death back to life by stitching together the component parts, thereby creating a living being who's life is desolation and isolation (being physically monstrous and also being the only one of its kind). Eventually, Victor pursues the creature it to the extremities of the earth in the Arctic Circle.

Victor, himself, becomes like ice as he becomes cold and cruel, wishing to destroy the life he created and becoming filled with hatred and despair. In the end, while in the Arctic Circle, as the creature endlessly evades Victor and Victor relentlessly pursues the creature, they become completely isolated from the rest of the world—frozen in a perpetual chase.

The ice symbolized the coldness and desolation that Frankenstein's monster feels in his loneliness. Victor, his creator, has rejected him. Other humans have recoiled from him in horror at his appearance. There is nobody else like him on the Earth. To the monster, the desolate Arctic wasteland, full of ice and empty of people, provides a refuge from the cruelty with which he has been treated.  

The cold, barren landscape, a place of glaciers and caves of ice, symbolizes how Frankenstein's monster feels inside after his rejection by mankind. He is desolate. Victor has even destroyed the companion he promised to make for the monster.

It's poignant, sad, and an indictment of how humans judge by external appearances that the monster finds the icy territory he now inhabits kinder to him than the human civilization he has fled. He prefers isolation to the pain of rejection. He tells Victor:

The desert mountains and dreary glaciers are my refuge. I have wandered here many days’ the caves of ice, which I only do not fear, are a dwelling to me, and the only one which man does not grudge. These bleak skies I hail, for they are kinder to me than your fellow-beings.

The use of ice in Frankenstein has several purposes. First, it adds to the sensory elements that are needed to understand, both, the setting as well as the atmosphere of specific chapters in the novel. The part of the novel where ice is more evident at the beginning, when Captain Walton's boat is exploring the Artic and encounters ice. There, the captain and crew see the monster sledding on an iceflo from a distance. Shortly after, he rescues Victor. This is when Victor confesses his story to Walton. 

Here we see that the ice is a perfect symbol to represent the fate that Victor's life has taken. Victor's fate has led him to a life that is fruitless, barren, frozen in time, and inevitably miserable. In the frigid and lonely Artic, there is nowhere to go, nor nothing, to do but to chase, or be chased. This is the case between Victor and the creature. This particular chase begins in Switzerland, when Victor determines to kill the creature. The chase crosses country boundaries and ends up in the Artic circle, where the are found at the beginning of the story. As it goes on, the creature seems to lure Victor to that very cold and freezing spot. This is evident in one of the notes that the creature leaves for Frankenstein just to elevate his chagrin.

My reign is not yet over — you live, and my power is complete. Follow me; I seek the everlasting ices of the north, where you will feel the misery of cold and frost, to which I am impassive.

Here we note that the monster actually wants to lead Victor to a cold, desolate, barren and "dead" place, in hopes that Victor succumbs to it. The idea of darkness, coldness, and isolation is also a Gothic element of narrative. Hence, it would also be a representation of Victor's fate and of his own soul.