As the seasons turn, so changes the experience of picking up dog poop. The following is based on residence in temperate North America.

SPRING
Plus: Spring in general smells good, and this helps improve the experience of handling your dogs' fresh, stinky turds.
Minus: It is probably raining. Wet turds are gross even if you can't smell them clearly. (NB: In very early spring, i.e., the thaw, retreating snow reveals three months' of other dogs' abandoned poop.)

SUMMER
Plus: ???
Minus: Temperature of poop rises after leaving the dog. Risk of glop is high, stink factor increased.

AUTUMN
Plus: Autumn smells are generally earthy and mask poop odor. Turds generally stable at average fall temperatures.
Minus: Dogs snuffling in leaves after dropped Halloween candy cause you to stumble and lose sight of leaf-colored turds. In the dim light, you will not be able to find them again, and you must walk away in shame as Bad Neighbor.

WINTER
Plus: Turds freeze on impact with the snow, making them nearly odorless and easy to handle. Visual contrast between turd and snow is also high.
Minus: It's fucking freezing out, and the only sensation you have in your hands is one of pain.
Plus: The fleeting heat of the poop may actually warm your fingers somewhat.
Minus: That's disgusting.