InDesign allows you to easily add color to a placed image, with certain restrictions:
The image must be saved as a grayscale or bitmap image. (Choose Image > Mode > Bitmap or Image > Mode > Grayscale in Photoshop).
The image must be saved in PSD, TIF, BMP or JPG format.
If the image is in PSD format, it may contain multiple layers, but the bottom layer must be opaque. In other words, you cannot apply color to a PSD image with a transparent background in InDesign.
To add color to an image, select the image with the Direct Selection (white arrow) tool, and then select a color from the Swatches palette or the Color palette.