Of the Lawson books, Mr. Revere and I was the big hit in our house; the Ben Franklin book never quite caught on. Lizzie went through a brief horse period, and we probably read it then. I loved it: lots of history and excitement. The horse was very far from being a naturalistic horse: she had strong political loyalties, first to the British, then to the revolutionaries. I remember being shocked some years later to discover that Revere's horse wasn't named Scheherazade as she was in the book.
As to your question about animals in books, there are many gradations of anthropomorphizing. There are the Wind in the Willows and Winnie-the-Pooh animals who, as you point out, are just a clever way to present people to kids.
As one gets further into chapter books, there are a number of series that create complex chivalric social structures, with clans, territories and wars, in worlds inhabited by animals. The
Redwall series by Brian Jacques (pronounced Jakes -- honest!) is the best-known of these. Jacques wrote 22 of them: mice, badgers and squirrels are the good guys; rats, foxes and weasels are their enemies. Character tends to be determined by species. I've only read one of them, but we carry them all -- as one gets further into the series the quality varies more. There are other series along similar lines focusing on house cats which have escaped to the wild (Warriors, by Erin Hunter), its spinoff about bears (Seekers) and Guardians of Ga'hoole by Kathryn Lasky, about owls. They're all quite popular with the middle-grade crowd.
The one our family got hooked on for a while was the Silverwing series, by Kenneth Oppel. It's four books about bats and includes a fair amount of behavior and information true to real bats. Different types of bats are distinguished from each other, and the hibernation season figures in the plot. The first book centers on the bats believing that they've been banded for a greater purpose. The purpose turns out to be nefarious human schemes.
Then there are the animals who act pretty much as animals yet interact with people -- dogs dominate this category. I'm thinking of two wonderful classics of the must-get-back-to-my-human genre:
The Incredible Journey by Sheila Burnford is the story of two dogs and a cat who cross hundreds of miles of Canadian wilderness to find their old home where they believe their family is. They go through all sorts of adventures and hardships on the way, but they're all things that really could happen. And
Lassie Come Home by Eric Knight is a wonderful story that has nothing to do with the American TV Lassie. Lassie belongs to a family in Yorkshire, but they're forced to sell her to someone who takes her to Scotland. She treks across Scotland and England to get back to the family. Most of the action in the book follows Lassie, but we cut back to the family occasionally. It's very intense, both in the feelings between the boy in the family and the dog, and in her series of scary and harsh experiences during her odyssey home.
Given the thousands of kids' books with animals in them, I know I'm missing lots of other categories. But there's a start.