In this paper, the zero-forcing (ZF) precoder with max-min power allocation is proposed for cell-free millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems using low-resolution digital-to-analog converters (DACs) with limited-capacity fronthaul links. The proposed power allocation aims to achieve max-min fairness on the achievable rate lower bounds of the users obtained by the additive quantization noise model (AQNM), which mimics the effect of low-resolution DACs. To solve the max-min power allocation problem, an alternating optimization (AO) method is proposed, which is guaranteed to converge because the global optima of the subproblems that constitute the original problem are attained at each AO iteration. The performance of cell-free and small-cell systems is explored in the simulation results, which suggest that not-too-small fronthaul capacity suffices for cell-free systems to outperform small-cell systems.