Yes, they do. but that's an old old issue. I know that one without bringing out a book. It's because of this place's past, before this world woke from its slumber.

[She pulled out something that seemed at least a little appropriate, setting it down on a stand and opening it.]

The deers were the protectors of the sleepers within the nightmare, the guardians of the town, totems and agents of the first of sleepers, Ramona Derwin. They were also those sleepers who had remained so long that they lost their memory and being, becoming nothing more than her agents, her tools and weapons.

I suspect that their souls continue to linger on as deer here, still protecting the world they preserved while it slumbered.