Gas: In addition to oxygen, summer gas has "heavier" components, so the vapor pressure is about the same in summer as winter gas "lighter" components in the winter. Essentially, in order to start the engine you want the right percentage of gas vapors in the gas/air mix.
Diesel: 20 years ago when I worked in this area, the right terminology was "cloud point". As temperature is lowered, wax crystals form in the fuel and it starts to look cloudy. The wax burns just fine if it is dissolved in the fuel, and actually has more energy. The problem is that it will clog the fuel filter.
Winter blends have less wax, and a lower cloud point.
If I had to use only one fuel year round, I would pick winter fuel in both cases, because it will start easier.
Neither winter or summer gas will stay fresh for a whole season, much less a year. I always add Stabil. Most of the time I add twice what they say to add. I would much rather spend a few bucks on gas stabilizer than spend 20 minutes trying to start a reluctant small engine.
The only diesel additive worth using is something to prevent algae in stored fuel. I have been to the research departments at Mack, Cummins, Caterpillar, and Yellow Freight, and they all agreed on that issue.