I would use felt to make the "saddle" and "blanket, black elastic for the "girth". I believe Walmart has 12"x12" felt squares that may work depending on the size of your dog. You may want to double or fill the "blanket". And, I'm sorry but I have no idea for the head piece :/ Posted via Mobile Device
For the red head thing I would use a tshirt and sew it up however I needed it.
Saddle Pad: I'd use felt or maybe a sweatshirt (since its heavier)
Girth: black shirt or a black elastic belt if you can find one.
Saddle: maybe some flexible cardboard/cardstock. Or you might be able to find something leather for cheap at a thrift store. The one I used to work at often had leather pants that would probably work. Then just cut it however you want.
Sew the saddle pad to the saddle and the girth to the saddle maybe? You could make a buckle thing to tighten it.
To hold it all together it looks like they used yarn, black rope or shoe lace. You might need hole protectors or whatever they are (the silver rings that help reinforce the hole so the fabric doesnt rip or stretch around it).
So yah all that stuff you could get at a thrift store :)