Is an exam required before a patient can be treated in New Mexico?

Short answer
Yes, for nurses in aesthetic healthcare facilities — an APRN or other licensed independent practitioner must examine the patient face-to-face (telemedicine may satisfy this), diagnose and set a treatment plan first; that can never be delegated.

New Mexico puts the exam beyond delegation in so many words. Before any aesthetic healthcare procedure, an APRN or other licensed independent practitioner must conduct a FACE-TO-FACE assessment, determine a diagnosis and prescribe a treatment plan — and "may never delegate the examination, diagnosis, or treatment plan". The initial examination must review the health history and physically examine the treatment sites. For continuing patients the face-to-face is required at least once every twelve months, and sooner on any change in health status or treatment plan. Telemedicine is permitted for that examination, provided the video quality does not adversely affect the assessment or diagnosis. Where a medical assistant runs the device, the supervising physician must personally supply the history, physical examination, diagnosis, treatment protocol and record before treatment begins.