Unfortunately, the original texture cannot be preserved after subdivision in SYNCHRO

If you wish to use the original texture, please subdivide the model in the original modeling program.

Otherwise, you may use Edit>Color to apply a representative color to the subdivided objects instead of gray.

If you have an Iray license, you may apply a material to the subdivided objects to appear in Iray renderings in 3D Properties>Raytrace Material.