We don't see much of Mrs. Z. She's Homer Zuckerman's wife and Fern's aunt, but she spends most of her time indoors. And since most of this novel takes place in the barn, she doesn't get much airtime. Basically, she spends her days in the kitchen or thinking about freezers. She's super obsessed with freezers. Why? Well she's probably got a lot of things to preserve on the farm, so that they have food for the winter. We're thinking this means Mrs. Z is a smart and resourceful lady.
(Quick brain snack: the first freezer was invented around 1913, but they didn't become common household items until decades later. So, Mrs. Z might be so into her freezer because it's new.)
And here's some more evidence to show us that she's resourceful and smart: Mrs. Z's main event in the novel is when she gives Wilbur a buttermilk bath before the fair. This makes him as clean as he's ever been. We may not see much of Mrs. Z, but she sure does make a big difference when it comes to Wilbur winning that special prize.