For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option

https://devinjgpe949.iamarrows.com/why-your-salt-lake-city-mini-split-may-ice-over-in-winter

For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option, especially where existing heating is radiant, hydronic, or space-heater based.