Stellar winds from fast-rotating Population III (Pop III) stars have long been suspected to make important contributions to early metal enrichment, as features in the nucleosynthesis of such 'spinstars' are consistent with the chemical abundance patterns of some metal-poor stars in the local Universe. Particularly, stellar winds rich in light elements can provide another pathway towards explaining the carbon enhancement in carbon-enhanced metal-poor (CEMP) stars. In this work, we focus on the feedback of Pop III stellar winds combined with supernovae (SNe), and derive the resulting chemical signatures in the enriched medium. We explore a large parameter space of Pop III star formation and feedback with a semi-analytical model. The predicted pattern of carbon and iron abundances of second-generation stars agrees well with observations of CEMP-no stars ([Ba/Fe] < 0) at [Fe/H] −3 and A(C) 7, under the optimistic assumption of significant mass loss by winds. In this scenario, carbon-rich but ironfree second-generation stars can form in systems dominated by enrichment from winds, gaining trace amounts of iron by accretion from the interstellar medium, to become the most iron-poor and carbon-enhanced stars seen in observations ([Fe/H] −4, [C/Fe] 2). Wind feedback from Pop III spinstars deserves more detailed modelling in early cosmic structure formation.