Metal halide perovskite (MHP) nanowires such as hybrid organic-inorganic CH3NH3PbX3 (X = Cl, Br, I) have drawn significant attention as promising building blocks for high-performance solar cells, light-emitting devices, and semiconductor lasers. However, the physics of thermal transport in MHP nanowires is still elusive even though it is highly relevant to the device thermal stability and optoelectronic performance. Through combined experimental measurements and theoretical analyses, here we disclose the underlying mechanisms governing thermal transport in three different kinds of lead halide perovskite nanowires (CH3NH3PbI3, CH3NH3PbBr3 and CsPbBr3). It is shown that the thermal conductivity of CH3NH3PbBr3 nanowires is significantly suppressed as compared to that of CsPbBr3 nanowires, which is attributed to the cation dynamic disorder. Furthermore, we observed different temperature-dependent thermal conductivities of hybrid perovskites CH3NH3PbBr3 and CH3NH3PbI3, which can be attributed to accelerated cation dynamics in CH3NH3PbBr3 at low temperature and the combined effects of lower phonon group velocity and higher Umklapp scattering rate in CH3NH3PbI3 at high temperature. These data and understanding should shed light on the design of high-performance MHP based thermal and optoelectronic devices.