The worst time of year is when all the dog shit thaws and the lawn turns into a giant cesspool. At least that's what happened with our two dogs out there taking dumps all winter and our three kids breaking their promises of "I'll pick up after them, dad... I promise"
We switched our dogs to a raw meat diet a few years ago (for health reasons). Although it's expensive, the biggest upside is that their shit doesn't stink anymore and it just dries up and crumbles. Haven't picked it up in years
The last few winters I've made it a point to pick up any and all dog poop that I see in the back yard, because the first year we owned the house I was lazy during the winter and paid for it in the spring haha. Of course a few are missed due to snowfall but what a difference in the spring if you've been dilligent about it.
Our ex neighbours were lazy with their english bulldog, and that girl could POOP...I mean like human sized piles. Their yard looked just disgusting in the spring and the smell was quite bad also.