This was a book for younger children that I borrowed repeatedly from the library in the early 1970's in the UK. All I can remember are the first few lines:
“It wasn’t a cold day. It wasn’t a hot day. It was a day just right for climbing a mountain.”
I know it was a picture book, but I have no more idea about what happened in the story.
I’d love to track it down if possible.
I’ve asked my mother if she can remember any more details. Apparently they carved their initials into a tree at the top of the mountain (which we heartily disapproved of).