I'm referring specifically to a letter he supposedly wrote to Kenneth Grahame in 1909 where, regarding The Wind in the Willows, Roosevelt stated he "read it and reread it, and have come to accept the characters as old friends."
I suppose this is multiple questions.
Wasn't he too busy with presidential duties to be rereading books for fun? If I've got my dates right, the book was originally published in October 1908 and Roosevelt's letter was written in January 1909. I understand this was as his presidency was nearing its end, but... surely there were still things to do in those months that would have been prioritized over befriending Mole and Badger, etc.
I though maybe he was reading it to his children, but the book was written from stories told to the author's four year old child and Roosevelt's children were older. I think the youngest would have been around 11 at the time.
How did he end up with a copy of it so early? Was it normal for the president to receive copies of new publications like this?
Perhaps I misunderstand and he only read it twice? Perhaps I misunderstand what was normal to read at the time?
Unlike Wilson (who said "I wonder if I am the slowest reader in the world" and it has been speculated he had dyslexia) Roosevelt was an absolutely prolific reader, and we can get a sense of his amount of reading from a timetable from an aide's diary from when he was campaigning for his first term in office.
7 am: Breakfast / A speech
8 am: Reading a historical work
9-11 Speech / dictating letters / Discussing Montana mines / another speech
Noon: Reading an ornithological work / speech
1: Lunch / speech
2: Reading Sir Walter Scott
3: Telegrams / speech
4: Meeting press / Reading
5: Speech
6: Reading
7: Supper
8: Speaking
11: Reading
Midnight: Bed
While in college he did activities one might stereotypically associate with Roosevelt (like boxing, hunting, and heavy drinking) he also took part in poetry reading, and a 1916 biography noted that during college "if he were reading, the house might fall about his head, he could not be diverted."
Roosevelt also wrote at length about book-reading, and he certainly had a wide spectrum of recommendations.
Books are almost as individual as friends. There is no earthly use in laying down general laws about them.
He highlights specifically when asked about books statesmen should read, that they should read poetry and novels, and while he hedges after, it is very inclusive, not just "books on history and government" but Greek drama and science. Roosevelt even credits his well known adventurous streak to reading; he had bad health as a child (with severe asthma attacks) and resorted to prolific reading as an escape, where he "felt a great admiration for men who were fearless and could hold their own in the world, and I had a great desire to be like them."
When The Wind in the Willows was published the President sent not one but two letters to Kenneth Grahame, as can be read here at the Bodleian. The first one in particular gives a strong hint as to your answer reading "books for children":
The book hasn't come, but I have never read anything of yours yet that I haven't enjoyed to the full. I am safe in thanking you heartily in advance.
In other words:
a.) he was a fan of his books before, which were not written for children; The Golden Age and Dream Days were reminiscences of childhood but targeted at adults and
b.) he received a very early copy and was in direct correspondence with the author before it even came out
While the book did have to receive defense as being "just for children" (notably Milne in a later edition) it was in good company, as the 1900s in England had quite a large number of serious works of children's literature, like The Jungle Book, The Secret Garden, and Peter Pan.