I’m not sure if I’m missing something somewhere, but I don’t see anywhere saying a deer, for example, wouldn’t be affected by underbrush in the forest. At the table the other day, there was an owlbear (I know, not an animal) fight and it was unhindered by the difficult terrain. It devolved into a conversation about whether or not animals got free stride abilities in the place they make home. We see some logic to them adapting to their home in such a way, but didn’t know if there’s any RAW supporting it.