Even the most southern parts of NM experience sub-freezing (below 32 degrees) overnight temps from December through February but it's doable if you don't mind cold weather camping. In AZ along the Colorado River and from Phoenix area onward south will have an abundant amount of places to RV, whether they meet your budget will require further investigation. Keep in mind that AZ is not nearly as far south as parts of Texas or Florida and will at times incur short periods of cold weather that happen to dip down into the southern regions of the Grand Canyon state during the winter season.