The levelized cost of heat (LCOH) and the technical feasibility in the specific context of building construction or renovation are the major drivers of users’ choices for space heating and cooling solutions. In this work, the LCOH was assessed for the most diffused heating technologies in Piedmont (NW Italy): that is, fossil fuels (methane, heating oil and liquefied petroleum gas—LPG), wood biomass (wood logs and pellet) and heat pumps (air-source and ground-source), both in heating-only and in a heating and cooling configuration. A sensitivity analysis of the main LCOH drivers was performed to assess whether and how each technology is vulnerable to energy price and upfront cost changes. The results show that heat pumps are competitive against gas boilers, but they are heavily dependent on refurbishment incentives and penalized by the high electricity prices in Italy; on the other hand, wood biomasses are competitive even in the absence of incentives. The analysis confirmed that LPG and heating oil are no more competitive with renewable heating. Acting on the taxation of natural gas and electricity is key to making heat pumps the most economically convenient solution to cover the heating and cooling needs of buildings.