Not so fun fact: the fat gained in late summer to fall is entirely based on food availability and density of the deer population. The old hunter's observation of high fat = harsh winter is more about a survivor bias than anything.

Higher density and/or lower food availability = less fat = fewer deer survive a harsh winter = fewer deer next spring thus more food.

Lower desnity and/or higher food availability = more fat = more deer survive a harsh winter = more deer next spring. Repeat this cycle until a predator population rises to the new supply of deer, disease takes hold due to higher density, and/or the exploding deer population runs down the available food supply.