Pain assessment is a hot topic today. As pain is perceived differently by each person and there are cases incapable of communicating it, automatic methods for pain classification based on machine learning (ML) are in constant development. Physiological signals, such as the Electrocardiogram (ECG), the Electrodermal Activity (EDA), and the Electromyogram (EMG) have been used in this context. However, there is a lack of documentation on the interpretability and explainability of its features in pain assessment. Thus, this work aims to evaluate the impact of features extracted from physiological signals in pain recognition. The data was collected during a protocol for pain induction using a Cold Pressor Task with previous emotional elicitation. Three different ML algorithms (Random Forest, XGBoost, and ADABoost) were trained using 17 features. Then, three explainable Artificial Intelligence (xAI) methods (the KernelSHAP, the SP-LIME, and the Morris Sensitivity Analyses) were applied to each of the three classifiers to select the most relevant features for each model. The ML algortihms were trained again using only the five most relevant features obtained with each xAI method. The results showed that the best accuracy is obtained by combining XGBoost + KernelSHAP. However, Random Forest + Morris Sensitivity provides fewer False Negatives. Moreover, the amplitude of the EMG of the trapezius and triceps muscles and the maximum and minimum value of the tonic component of the EDA were highlighted by the xAI methods.