The wetting characteristic of micro-droplets on surfaces with different free energies is crucial to heterogeneous nucleation theory and the growth mechanism of micro-droplets during vapor condensation. In this paper, the spreading processes and wetting characteristics of nanoscale water droplets on various surfaces are explored by molecular dynamics simulation method. The surfaces are constructed from face centered cubic copper-like atoms with different Lennard-Jones potential parameters. The Lennard-Jones interaction energy well-depth of the surface atoms is adjusted to acquire different surface free energies, and the ratio of surface-water interaction energy well-depth to the water-water interaction energy well-depth is defined as the interaction intensity. In the present study, the relationship between interfacial free energies and solid-liquid interaction intensities is evaluated using molecular dynamics simulations. The wetting characteristics of TIP4P/2005 water droplets on surfaces with various free energies are simulated and analyzed as well, using molecular dynamics simulations under an NVT ensemble. Results indicate that the solid-liquid interfacial free energy increases as the solid-liquid interaction intensity increases, with different spreading processes and wetting characteristics achieved for the water droplets on these surfaces. For the surfaces with lower interaction intensities, water cannot spread on the solid surfaces and hydrophobic surfaces are obtained when the interaction intensity ratio between surface atoms and water molecules is lower than 1.6. As the interaction intensity increases, the surface translates from hydrophobic into hydrophilic, and finally into a complete wetting state as the interaction intensity reaches up to 3.5. Due to the limitation of nanoscale dimensions, the forces that exert on droplet surface are non-continuous and asymmetric. As a result, significant fluctuations of liquid-vapor interface and local solid-liquid contact line can be observed for the droplet in nanoscale. The transient contact angle of nano-droplets is also fluctuating within a certain range, which is different from that observed for macro-droplets. From the viewpoint of statistics, an apparent contact angle can be obtained for the droplet on each surface. The contact angle decreases with solid-liquid interaction intensities linearly, which is in accordance with the calculated results of classic Young's theory using the interfacial free energies obtained from molecular dynamics simulations. The fact that an apparent contact angle is already established for a droplet in nanoscale, supporting the capillary assumption that is widely adopted in classic nucleation theory. The fluctuation of liquid-vapor interface and contact angle also provides a qualitative explanation for the discrepancy between experimental nucleation rates and predictions in classic nucleation theory.