Use tempera or poster paint to paint the inside of your box. Paint the walls light blue to make your diorama's background. You can paint details like clouds or falling snow.
Paint the ground white for a snowy landscape. You can include a body of water to show how integral the sea is to polar life.
You can also paint the outside of the box, if you like. Use acrylic paint if your box has a glossy finish.
Make side, bottom, or center tabs for the rest of the animals. These will allow the animals to be attached to the bottom and/or sides of your box. There are a number of ways to make the tabs:
a.) L-shaped tabs - make an L-shaped paper tab and glue this at the back of the animal. Position the tab at the bottom edge of the animal to make a bottom tab or at the sides for a side tab.
Create blocks of ice or glaciers by gluing common household supplies like the ones below.