In my opinion? The dog didn't die from being left outside considering there's a doggy door Wu didn't feel like acknowledging until a year after the event. It was sick, went outside to seek help/greet Frank and Wu as they drove into the driveway and then something happened that made them believe Crash was unwell.
The problem is Wu's story makes even less sense now and seems like she hammed it up a bit over twitter before taking the dog to the vet which is where she finally realized the severity of Crash's issues. I don't think Wu locked the dog out to freeze or anything but I do feel like she played it up a bit before shit got too real. I mean, didn't she suggest Gamergate might have poisoned her dog at one point?