Vegetation height is a crucial factor in environmental studies, landscape analysis, and mapping applications. Its estimation may prove cost and resource demanding, e.g., employing light detection and ranging (LiDAR) data. This study presents a cost-effective framework for height estimation, built around texture analysis of a single very high-resolution passive satellite sensor image. A number of texture features are proposed, based on local variance, entropy, and binary patterns. Their potential in discriminating among classes in a wide range of height values used for habitat mapping (from less than 5 cm to 40 m) is tested in an area with heath, tree, and shrub vegetation. A number of missing data handling, outlier removal, and data normalization methods are evaluated to enhance the proposed framework. Its performance is tested with different classifiers, including single and ensemble tree ones and support vector machines. Furthermore, dimensionality reduction (DR) is applied to the full feature set (192 features), through both data transformation and filter feature selection methods. The proposed approach was tested in two WorldView-2 images, representing the peak and the decline of the vegetative period. Vegetation height categories were accurately distinguished, reaching accuracies of over 90% for six height classes, using the images either individually or in synergy. DR achieved similarly high, or higher, accuracies with even a 3% feature subset, increasing the processing efficiency of the framework, and favoring its use in height estimation applications not requiring particularly high spatial resolution data, as a cost-effective surrogate of more expensive and resource demanding approaches.