What about the birds?
As you may know (and was briefly mentioned in an “info” bubble earlier), it’s not quite true that all dinosaurs went extinct. There were a few small species that survived, and these are what we now call birds. In other words, birds are living dinosaurs!
How did birds survive the mass extinction? Most likely, in the same way as the small mammals. Just as many small mammals burrow and store food underground, so do some birds. These birds would therefore have had the same ability to survive the global winter as the small mammals, thereby explaining how they managed to survive.