So right, Drew. The leaf mulch will help a lot, but there is a double whammy keeping a fleshy tropical plant outdoors through your high desert winter, Antoinette. Cold plus dessication. You will have to make sure that plant doesn't dry out as well as keeping it from freezing. Terribly low humidity out there esp. in winter.
When we lived in Salt Lake City, the south side of my house was at least a zone warmer than the rest. It did get sun most of the afternoons in winter, and also got snow and snowmelt dripping off the roof above there. The house acts as a 'heat sink' collecting warmth in the daytime and radiating it at night. Plus of course on cold nights you are heating the house inside anyway, so some of that heat escapes.
i would think your best chance of keeping your Monstera going would be if you can situate it against a south-facing wall, and water it lightly at least once a week, plus a deep, moist mulch of leaves or other dark colored, insulating material. Peat moss might help, if you can't find a couple of wheelbarrows full of leaf mulch. But peat is hard to keep moist, and when it dries, it's hard to wet again as well.
