Slice cake horizontally into 4 equal layers. Place bottom cake layer on freezer-safe serving plate; spread with raspberry sherbet. Top with second cake layer; spread with lime sherbet. Top with third cake layer; spread with orange sherbet. Place fourth cake layer on top. Freeze until sherbet is firm, about 1 hour.
In large bowl, beat all frosting ingredients with electric mixer on low speed until soft peaks form. Beat on high speed until stiff peaks form, scraping side of bowl occasionally. Frost side and top of cake. Freeze until firm before serving, at least 30 minutes.