Recently, we have determined surface distributions of $alpha$ clusters in the ground state of $^{20}mathrm{Ne}$ from $alpha$-transfer cross sections, without investigating the properties of its excited states. In this paper we extend our comprehension of $alpha$-cluster structures in excited states of nuclei through reaction studies. In particular we focus on $^{16}mathrm{O}$, for which attention has been paid to advances of structure theory and assignment regarding $4^+$-resonance states. We study the surface manifestation of the $alpha$-cluster states in both the ground and excited states of $^{16}mathrm{O}$ from the analysis of the $alpha$-transfer reaction $^{12}mathrm{C}(^6mathrm{Li},d)^{16}mathrm{O}$. The $alpha$-transfer reaction is described by the distorted-wave Born approximation. We test two microscopic wave functions as an input of reaction calculations. Then a phenomenological potential model is introduced to clarify the correspondence between cluster-wave functions and transfer-cross sections. Surface peaks of the $alpha$-wave function of $^{16}mathrm{O}(0^+)$ are sensitively probed by transfer-cross sections at forward angles, while it remains unclear how we trace the surface behavior of $^{16}mathrm{O}(4^+)$ from the cross sections. We are able to specify that the $alpha$-cluster structure in the $0_1^+$ and $0_2^+$ states prominently manifests itself at the radii $sim 4$ and $sim 4.5$~fm, respectively. It is remarkable that the $4_1^+$ state has the $^{12}mathrm{C}+alpha$-cluster component with the surface peak at the radius $sim 4$ or outer, whereas the $^{12}mathrm{C}+alpha$-cluster component in the $4_2^+$ state is found not to be dominant. The $4_2^+$ state is difficult to be interpreted by a simple potential model assuming the $^{12}mathrm{C}+alpha$ configuration only.
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