[TOMT][BOOK][90's or Early 2000s] Snow Bunny/Rabbit or Mouse Book

There was a book I read years ago in either 2004 or 2005. I was in Pre-K when I read it. I was really young (born in 2001), so I can't remember the plot. All I know is that it was about a bunny/rabbit or possibly a mouse who builds a snowman. I can't remember what animal the main character it, but I believe it was a small rodent. It was a picture book for kids.

Also, the snowman itself was also possibly a bunny/rabbit or mouse. It didn't look like a normal snowman.

It isn't Snow Bunny's Christmas Wish, as it was published in 2013. It isn't Snow Bunny's Christmas Gift, as it was published in 2015. At first, I thought it was Snow Bunny's Christmas Gift as the cover looks familiar, but that book came out years after I read the book I'm looking for. It also isn't Mouse Loves Snow or Snow Mouse.

Edit: I don't believe it was part of a series. I think it was a standalone book, but I could wrong.