(1) Background: Some cancer patients do not experience tumour shrinkage but are still at risk of experiencing unwanted treatment side effects. Radiomics refers to mining biomedical images to quantify textural characterization. When radiomics features are labelled with treatment response, retrospectively, they can train predictive machine learning (ML) models. (2) Methods: Radiomics features were determined from lymph node (LN) segmentations from treatment-planning CT scans of head and neck (H&N) cancer patients. Binary treatment outcomes (complete response versus partial or no response) and radiomics features for n = 71 patients were used to train support vector machine (SVM) and k-nearest neighbour (k-NN) classifier models with 1–7 features. A deep texture analysis (DTA) methodology was proposed and evaluated for second- and third-layer radiomics features, and models were evaluated based on common metrics (sensitivity (%Sn), specificity (%Sp), accuracy (%Acc), precision (%Prec), and balanced accuracy (%Bal Acc)). (3) Results: Models created with both classifiers were found to be able to predict treatment response, and the results suggest that the inclusion of deeper layer features enhanced model performance. The best model was a seven-feature multivariable k-NN model trained using features from three layers deep of texture features with %Sn = 74%, %Sp = 68%, %Acc = 72%, %Prec = 81%, %Bal Acc = 71% and with an area under the curve (AUC) the receiver operating characteristic (ROC) of 0.700. (4) Conclusions: H&N Cancer patient treatment-planning CT scans and LN segmentations contain phenotypic information regarding treatment response, and the proposed DTA methodology can improve model performance by enhancing feature sets and is worth consideration in future radiomics studies.