God of war 1 2 and 3 are all about how this savage, violent, unrepentantly vindictive demigod with a history of incredible violence is trying to escape the visions of madness that torment him, only to be used and disenfranchised by the greek pantheon, which he then single handedly kills in a fit of terrible rage, but before he dies he gives what's left of the smoldering, flood, tornado and spirit-scoured crater that is greece the gift of hope before leaving for new lands.
Enter the norse mythology, his backstory is that he met laufey, had a kid and then she died, so he takes his son on a long pilgrimage to bury her ashes in joutunheim. in the beginning of the game we see that kratos made his son a bunch of toys and later he even loans atreus his axe as he tries to enter the light of alfheim. though unintentional, he also gave the light elves the gift of liberation from the dark elves. Years after this he would go on to participate in ragnarok against his will, drawn into the conflict by his son's pursuit of tyr, the ancient god of war. kratos is credited by the midgard people as the source of fimbulwinter as he killed baldur, they outright call him "the winter man" so he is already regarded as god associated with winter. throughout his journey he helps people with many problems and even gives the long-warring elf tribes a real chance at peace. he kills dragons and cleanses a valley, letting it grow and develop into a verdant paradise. he has now begun working tirelessly to make the world a better place, a place where peace can reign and evil gods such as odin can't rule the weak with an iron fist. but he even goes so far as to try to save his chief rival in this conflict, thor, and manages to convince him to stand down before odin kills him for his defiance.
One of the sidequests of ragnarok specifically involves him guiding primordial deer back to the world tree that they might continue their work maintaining its boughs to avoid the tree ever buckling.
for his role in ragnarok the valkyries and freya want to make him the new god of war of the norse pantheon, but kratos understandably has misgivings so he, under tyr's tutelage, chooses to confront his dark and wrathful past, not to forgive it, but to understand the roots of his violence so that he might better change and avoid making such mistakes in the future. by the end of it he finally comes to terms with himself and chooses to become the norse pantheon's new god of war, to ensure peace and civility can reign supreme.
What we're experiencing across the entire franchise is a massive multi-game leadup to kratos one day adopting the mantle of a peaceful god who makes gifts for children and brings happiness and prosperity every winter, normally a time of death, that he might make the world a better place. it's why he's growing the beard and why they have him wielding a winter-themed axe.
Soon kratos's next mainline game will feature him collecting godlike reindeer and teaming up with a seemingly evil god called krampus to save the world from cthulhu, afterwards in order to keep the eldritch monster at bay kratos and krampus will create a holiday, kratos will reward good children and encourage good behavior, and krampus will punish the bad ones that they change their evil ways so that cthulhu can't use their evil to infect the world with his power. in this way kratos will become santa claus. we're just seeing the entire origin leading up to a big christmas payoff. but this also means that someone at santa monica needs to be brave enough to create the game where kratos gets into a fistfight with jesus as the direct lead-in to "god of christmas" the final game in the god of war franchise!!
EDIT: Oh no what have I unleashed....
