We present Timber, the first white-box poisoning attack targeting decision trees. Timber is based on a greedy attack strategy leveraging sub-tree retraining to efficiently estimate the damage performed by poisoning a given training instance. The attack relies on a tree annotation procedure which enables sorting training instances so that they are processed in increasing order of computational cost of sub-tree retraining. This sorting yields a variant of Timber supporting an early stopping criterion designed to make poisoning attacks more efficient and feasible on larger datasets. We also discuss an extension of Timber to traditional random forest models, which is useful because decision trees are normally combined into ensembles to improve their predictive power. Our experimental evaluation on public datasets shows that our attacks outperform existing baselines in terms of effectiveness, efficiency or both. Moreover, we show that two representative defenses can mitigate the effect of our attacks, but fail at effectively thwarting them.