Mini-split cold weather efficiency study by CARB

techntrek

Some interesting findings.  They may not be as efficient as manufacturers claim.  You get the best efficiency by leaving them on "auto" and not "low".  Setting the temperature back affects the overall efficiency.  Running it to its maximum capacity get the best efficiency (not as efficient as supplemental heat).

On cost savings:  “Even with lower efficiencies than published in other studies, most of the heat pumps still provided heat at a lower cost than oil, propane, or electric resistance systems. … None of the ASHPs monitored would have provided operating cost savings over an efficient natural gas heating system.”

http://www.greenbuildingadvisor.com/articles/dept/musings/ductless-minisplits-may-not-be-efficient-we-thought