We investigate the role of uncertainties due to the use of nuclear data when determining proton parton distribution functions (PDFs), and show how these uncertainties can be included in fits. In particular, we assess data with nuclear targets included in NNPDF3.1, namely from CHORUS, NuTeV and E605 with Pb, Fe and Cu targets respectively. We then analyse the resulting form of the PDFs, noting that the increase in uncertainty is small. Finally, we consider the impact on the $\bar{d}/\bar{u}$ ratio, total strangeness $s + \bar{s}$ and strange valence distribution $s - \bar{s}$. We find the effects to be negligible in all cases.