I don't know about 'Cheap', but I'd look into old conveyor belting from a factory or mine or quarry.
Lots of times they will give the old stuff away just to get someone to haul it off.
Someplace that repairs conveyors will have belting laying around you can scarf up for little or nothing.
You might look for an old barn or house being taken down that has metal roofing.
Since you aren't trying to use it to keep water out of the house, the nail holes won't matter and you would be able to get that for cheap.
Metal sheeting at the recycled home places is dirt cheap.
They take it off buildings, roofs, ect. and try to resell it instead of scrapping it, but most people want it for roofing, so they don't want nail holes.
Usually sold for scrap weight when you find it, so it's very cheap.
If you need insulation from the cold, the Styrofoam board from the lumber yard or even straw bales (which are more expensive than Styrofoam now and rot)
Will work for insulation behind the conveyor belting or tin outside.
I agree with Jeep Hammer, the aluminum roof or side paneling, is inexpensive and will keep the varmits out also, a cat can walk right through a garbage bag.
Also, install it with the ribs standing vertically (this is strong) and use a simple treated 2"x2" frame layed out 4' on center. Leave an access entry.
Use screws instead of nails.
reviving a 2 month old thread. has anyone thought of square bailed hay. Ive seen camping trailers completely covered including the roof for insulation. probly not a good idea to thump cigerette buts around tho. it wont keep the small varments out either but very comfy and dark!!
How long do you want them to last? On the short term, you could just stack straw/hay bales. However, animals will feed on hay... straw has no food value. If you want them to last, look into straw bale building techniques... learn about pre-dipped bales. Dip them in plaster to coat the outside, then set them on a bit of foundation (concrete blocks, wood, etc) to keep them off the ground. The straw bales have a great insulating capability, and when coated in plaster, are very fire resistant. (much better than a stud wall).
don't know where you live but make sure you have atleast two vents in the skirting. If you don't it will stay moist under the trailer and cause mould to grow. If you live in a dry area you might not have to worry about this but I would check into it in your area.