We have performed $^{75}\mathrm{As}$ NMR measurements on single crystals to investigate the nematic behavior via the in-plane anisotropy of the electronic state at the As site far from Co impurities in the representative iron arsenides $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$. From the analysis of the angular dependence of the NMR satellites in the $c$ plane using the binominal distribution, we find that there is the in-plane fourfold symmetry breaking, namely, the orthorhombic-type anisotropy in the electric field gradient (EFG) at the As site with no Co atom at the nearest neighboring Fe sites even in the tetragonal phase of both ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ and $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}(x\ensuremath{\ne}0)$. The NMR spectrum in the antiferromagnetically ordered state of ${\mathrm{BaFe}}_{2}{\mathrm{As}}_{2}$ is shown not to support a nanotwin model on the basis of the nematic order proposed from the pair-distribution analysis of neutron scattering data. Based on results of the $x$ and temperature $T$ dependences of the in-plane anisotropy in the wide $x$ and $T$ ranges, the symmetry breaking is concluded to come from the local orthorhombic domains induced by disorder such as Co impurities or lattice imperfections. Furthermore, we find that the asymmetry parameter of EFG $\ensuremath{\eta}$ obeys the Curie-Weiss law which may be governed by nematic susceptibility, and the Weiss temperature becomes zero at ${x}_{\mathrm{c}}\ensuremath{\sim}0.05$ in $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$.