Anyone Heard of This Book?

[Don'tLiveonMoon]

My grandma had a book featuring a bear and a mouse (I think) who meet each other and want to be friends, but they run into a roadblock when they discover they have nothing in common. So it goes throughout the book, and they're about to give up on finding anything to do together when they discover that they both like to eat ice cream in the afternoon. I would guess that the book is from the 70s, maybe even earlier. I loved it as a child but can't recall the title for the life of me. Does it ring a bell to anyone?
Erin

 

[Fragglemuppet]

I thaught at the beginning it might have sounded familiar, but I'm afraid not. I'm sorry, I know how painful unattainable childhood memories can be!