Seasons in Grendel

I think the role of the four seasons in Grendel is interesting and confusing. We are introduced to Grendel in the spring. Initially, he observes human behavior and undergoes a change from pure beast to aspiring to project the traits of humans. Beowulf (and therefore Grendel) follows a traditional pattern, and traditionally, in literature, spring represents change and progression.
Grendel dies in the winter - traditionally the season for death, darkness, and endings. 
Does Grendel follow the traditional, stereotypical seasonal patterns? If so, what do summer and fall represent? If not, what role do the seasons play in his personal progression?