Place butter and brown sugar in a large bowl. Using an electric mixer, beat on medium speed for about 4 minutes or until pale and fluffy.
Add egg and vanilla extract. Beat until just combined.
Reduce the mixer speed to low. Add flour, baking soda and salt. Beat until combined.
Using your hands, bring the mixture together. Cover with plastic wrap and refrigerate until chilled through, about 30 minutes.
Preheat oven to 190 C / 375 F. Line two baking sheets with parchment paper. Set aside.
Depending on the size of the cookies you want, divide the dough into 10 big or 20 small portions. Divide each portion into two parts - one big (for snowman’s body) and one small (for head).
Roll and arrange on baking sheet to resemble snowmen.
Bake for about 10-12 minutes or until the cookies are golden around the edges and soft in the middle.
Remove from oven and let cool on baking sheets for 10 minutes. Then transfer to wire racks to cool completely.
Once cooled, dip one side of the cookies in melted white chocolate. Sprinkle grated coconut over the body of the snowmen.
When chocolate is set, use rainbow straps for the scarves and dark chocolate chips for the buttons. Cut small triangles from the rainbow straps for nose. Use black writing icing for eyes.