What is the best way to insulate a double shed door-

Probably not. Glass and/or plastic sheet goods really have no insulating factor. It will block the weather. It's like single glass pane windows. Put your hand on the glass and you can feel the heat or cold depending on the season.

buy styrofoam that is covered with insulation

I don't know how cold it gets in Kansas but an unheated space here in Maine would not be useable for an art studio. On our front door we have a double layered velvet curtain hung from rings that we use in the winter time on top of our front door which has a storm door in front of that. I would suggest layering even inexpensive fleece blankets maybe four or five deep and leaving loose for air to also insulate.

What are the doors made of and how do they open? If they swing open you can reinforce the hinges and frame out the inside to be insulated with fiberglass or foam. Then cover the inside framing same as you did walls. This would also be a good time to put some weather striping around the doors. If the doors slide to open, then it is unlikely that there is enough space to add anything that would make a difference. Anything can be done to wooden doors but metal doors are not usually strong enough for anything but foam board. Though not in your question I would suggest that you put down some flooring. There is a product that comes in 12 or 18 inch squares it has a layer of plastic that holds up a layer of OSB. It is a snap together sub floor designed as an air space that seperates a porous slab from carpeted or wood floors like in basements. You wouldn't need to cover it, but I think it would improve your warmth greatly. Nothing sucks the heat out of you like time spent standing on cold concrete.

Plexiglass is expensive. Home improvement stores sell 1" thick styrofoam panels cut 15 1/2" by 48". They are easy to cut-to-size using a utility knife (also sold at home improvement stores). Affix to the door with an adhesive like Liquid Nails.