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Vertical nanowire (NW) arrays are the basis for a variety of nanoscale devices. Understanding heat transport in these devices is an important concern, especially for prospective thermoelectric applications. To facilitate thermal conductivity measurements on as-grown NW arrays, a common NW-composite device architecture was adapted for use with the 3ω method. We describe the application of this technique to obtain thermal conductivity measurements on two GaAs NW arrays featuring ~130 nm diameter NWs with a twinning superlattice (TSL) and a polytypic (zincblende/wurtzite) crystal structure, respectively. Our results indicate NW thermal conductivities of 5.2 ± 1.0 W/m-K and 8.4 ± 1.6 W/m-K in the two samples, respectively, showing a significant reduction in the former, which is the first such measurements on TSL NWs. Nearly an order of magnitude difference from the bulk thermal conductivity (~50 W/m-K) is observed for the TSL NW sample, one of the lowest values measured to date for GaAs NWs.