Semiconductor lasers are strongly altered by adding spin-polarized carriers. Such spin lasers could overcome many limitations of their conventional (spin-unpolarized) counterparts. While the vast majority of experiments in spin lasers employed zinc-blende semiconductors, the room temperature electrical manipulation was first emonstrated in wurtzite GaN-based lasers. However, the underlying theoretical description of wurtzite spin lasers is still missing. To address this situation, focusing on (In,Ga)N-based wurtzite quantum wells, we develop a theoretical framework in which the calculated microscopic spin-dependent gain is combined with a simple rate equation model. A small spin-orbit coupling in these wurtzites supports simultaneous spin polarizations of electrons and holes, providing unexplored opportunities to control spin lasers. For example, the gain asymmetry, as one of the key figures of merit related to spin amplification, can change the sign by simply increasing the carrier density. The lasing threshold reduction has a nonmonotonic depenedence on electron spin polarization, even for a nonvanishing hole spin polarization.