If I buy a large appliance for my home (or know that someone in my family is about to) I keep the box to lay on top of the carpet in the room that I want to clean my harness (or saddles) in. I carefully cut the box open at one of the corners so that the entire surface of the box can be flattened (it stores nicely out of the way against the inside wall of the garage until needed).
Be careful of newspapers as even multiple layers are just not thick enough to prevent any real liquid from soaking through to whatever is underneath.
Also, you can check with a carpet and/or flooring store or a surplus building supply store for small (rug size) carpet and linoleum remnants. A lot of stores sell carpet remnants very, very cheaply (and you could use a carpet remnant for years) and they throw the trimmings from installations away (check their dumpster).