He doesn't even have a full Wikipedia article. Just a squib:
Old Man Winter is a personification of winter, sometimes also called Father Winter.What poems? We're not told. Dubious — discuss... that's harsh. Let's go over to the "personificantion" link, which is an article titled "Anthropomorphism," a great topic. I'm especially interested in the personifications that were once common and have withered away, perhaps because we're overwhelmed by commercial advertising branding a product with a character. These old-fashioned folk personifications have been ousted from whatever niche in the human mind they once occupied.
He may be an alternative older name for Father Christmas and has been identified with the Old English god Woden.[dubious – discuss]
Old Man Winter is referenced in several poems.
The "Anthropomorphism" argument looks back to the art of the Upper Paleolithic period, to figurines that that seem to suggest that people were conceptualizing nature in human terms, perhaps as a way to understand or control it. This concept leads to thoughts of gods....
Some religions, scholars, and philosophers objected to anthropomorphic deities. The Greek philosopher Xenophanes (570–480 BCE) said that "the greatest god" resembles man "neither in form nor in mind." Both Judaism and Islam reject an anthropomorphic deity, believing that God is beyond human comprehension...Speaking of Faces in the Clouds... Old Man Winter!
Hindus do not reject the concept of a deity in the abstract unmanifested, but note practical problems. Lord Krishna said in the Bhagavad Gita, Chapter 12, Verse 5, that it is much more difficult for people to focus on a deity as the unmanifested than one with form, using anthropomorphic icons (murtis), because people need to perceive with their senses.
In Faces in the Clouds, anthropologist Stewart Guthrie proposes that all religions are anthropomorphisms that originate in the brain's tendency to detect the presence or vestiges of other humans in natural phenomena.
Anyway, I still want to know what the Old Man Winter poems are. I looked, but I got waylaid at "An Old Man’s Winter Night" by the aptly named Frost:
One aged man—one man—can’t fill a house,
A farm, a countryside, or if he can,
It’s thus he does it of a winter night.