It is possible to obtain a sampled-data representation of a nonlinear dynamic system under zero-order hold using Taylor-Lie series. Within the context of Taylor-Lie series theory, explicit formulae for the resulting discrete-time system are derived in terms of the system Lie derivatives. The effect of sampling on system-theoretic properties, such as equilibrium properties, relative order, stability, zero dynamics and minimum-phase characteristics, is examined, revealing the natural and transparent way in which the use of Taylor-Lie series permeates the relevant theoretical aspects. The results derived are also illustrated in two chemical engineering examples.