Should I add page numbers to my picture book?

Yes! I can just imagine this conversation:

"Ok class, I'd like you to turn to the page with the deer...No, not that page, the one two pages before that one...No, the two pages the other way...The page that looks like this."

Or, "Ok class, turn to page 6." So much easier!

To me, as a retired teacher, having page numbers just makes sense. 

Since most of my books are 8.5 by 8.5 inches, I have a template created with the page numbers already added, so it's super convenient. Once and done sort of mentality. 

Page numbers should begin on the right hand side of your first spread, EVEN if the spread is a double spread. Odd page numbers on the right, even page numbers on the left.