CeCd$_3$P$_3$ and CeCd$_3$As$_3$ compounds adopt the hexagonal ScAl$_3$C$_3$-type structure, where magnetic Ce ions on a triangular lattice order antiferromagnetically below $T_\text{N} \sim$0.42~K. Their crystalline electric field (CEF) level scheme has been determined by fitting magnetic susceptibility curves, magnetization isotherms, and Schottky anomalies in specific heat. The calculated results, incorporating the CEF excitation, Zeeman splitting, and molecular field, are in good agreement with the experimental data. The CEF model, with Ce$^{3+}$ ions in a trigonal symmetry, explains the strong easy-plane magnetic anisotropy that has been observed in this family of materials. A detailed examination of the CEF parameters suggests that the fourth order CEF parameter $B_{4}^{3}$ is responsible for the strong CEF induced magnetocrystalline anisotropy, with a large $ab$-plane moment and a small $c$-axis moment. The reliability of our CEF analysis is assessed by comparing the current study with earlier reports of CeCd$_{3}$As$_{3}$. For both CeCd$_{3}X_{3}$ ($X$ = P and As) compounds, less than 40 \% of $R\ln(2)$ magnetic entropy is recovered by $T_\text{N}$ and full $R\ln(2)$ entropy is achieved at the Weiss temperature $\theta_{p}$. Although the observed magnetic entropy is reminiscent of delocalized 4$f$-electron magnetism with significant Kondo screening, the electrical resistivity of these compounds follows a typical metallic behavior. Measurements of thermoelectric power further validate the absence of Kondo contribution in CeCd$_{3}X_{3}$.