It could represent his corruption, his descent into the evil ways we are so familiar with from the main trilogy

He had the POTENTIAL to be like his mother. He MAKES the decision to be like his father later on, of course, but I really think that the once-innocent makeup compact that is a direct connection to his mother being filled with poison & used to kill is a really interesting piece of symbolism

It’s a reoccurring point in the novel that Snow can either take after his mom or his dad. Obviously he’s always been kind of a shit person from the start (he’s always been prejudiced, always been brainwashed, always been egotistical) but he still had the POTENTIAL to be good in the beginning

And then even later, in the main trilogy, Katniss says that Snow REEKS of rose perfume, to the point it’s nauseating. (We learn in Mockingjay that this is to mask the smell of the bloody sores in his mouth)

ANYWAYS!!! The makeup compact. It starts out as a security blanket, a source of comfort in pressing times. Then… at his direction, it’s filled with poison & used as a weapon by Lucy Gray in the arena

Snow associates his mother with good things. She’s described as loving, soft, & kind. On the other hand, his father is described as distant, cold, and hateful… but also protective, or at least Snow says he felt protected by him when he was alive

But the scent of the rose powder is a source of comfort for him. He smells it when he’s incredibly upset, or missing her. It’s his security blanket

Obviously the compact starts out as a security blanket of sorts. It’s probably the most personal item Snow owns, both because it’s a physical connection to his mother (since it was hers) & because it brings back fond memories of her before she died