Use plywood to make the box.
Line the inside surface with aluminium foil with shiny side to the wood.
Next use some heavy cardboard about ? inch thick next to the foil.
Put another layer of foil with the shiny side inwards.
Glue a layer of cotton wool to the outside and and wrap in plastic.
Make a lid in the same way.
Put the popsicle inside and seal the lid with duct tape.
very light wood like balsa, cardboard, or use double pane uv shielded thermal glass (then it would be clear)
the best insulator is a vacuum. this is the principle of the thermos bottle. a layer of glass next to another layer of glass separated by a vacuum is used in a DEWAR flask to keep liquid nitrogen from boiling.
most cryogens are stored in dewar flasks to prevent boiling (think 350 degrees below zero)
cork, sponge rubber