To avoid the licensing pitfalls, you can grab plenty of Landsat TM5/ETM7 data from GLOVIS. Then, using eg bands 3 and 4 (red and near-infrarred), and possibly others, you can try to classify the image, export as a polygon and then tweak the polygon to your hearts' content. For forests, using the spatial correlation between pixels is often very useful (in your example, look at the granularity of forest stands). Texture classifiers (for example, calculate the variance of NDVI over a 3x3 window) supplement the pure radiometric classifiers.
Regarding tools, GRASS has been mentioned as is probably a good choice. We have ENVI at work, and while not free software, it would be the tool I'd consider for this.
Note that the Landsat data are often contaminated by clouds or cloud shadow. You may need to dig a bit into the archive to find suitable data.