Preheat oven to 350 degrees. Line baking sheets with parchment paper.
In a medium bowl, combine flour, baking soda, and salt.
In a large bowl, beat butter and sugars until smooth. Add vanilla extract and eggs. Mix until combined. Slowly add flour mixture until dough forms. Fold in chocolate chips, cherries and walnuts.
Drop by 1 1/2 Tbsp amounts onto prepared cookie sheets. Bake for 9-11 minutes or until edges are set. Let cool on cookie sheet for 2 minutes and then transfer to wire cooling racks to cool completely.
In a small bowl, mix together powdered sugar and water until icing reaches desired consistency. Drizzle on cooled cookies and let set.