This work aims to study the capability of Sentinel-2 time series for classifying the spring season crops grown under Plastic Covered Greenhouses (PCG) in Almería (Spain). In 2018, our team published an article on greenhouse crop classification for the two typical cycles of intensive agriculture in Almería: autumn and spring. To this end, 1114 PCG were visited in the spring of 2017 to monitor the crops growing inside them. These crops were grouped into four classes: pepper, tomato, aubergine/cucumber and melon/watermelon. The well-known non-parametric decision tree classifier achieved an overall accuracy of 75.4% working on a dataset of six multi-temporal Sentinel-2 images taken during the spring of 2017. In this case, up to 55 features per image were used to feed the classifier. The corresponding classification F1-score values were 41.53%, 94.74%, 76.76% and 75.05% for aubergine/cucumber, melon/watermelon, pepper and tomato, respectively. Considering the aforementioned results, a battery of classifiers, such as efficient logistic regression, linear discriminant, or feedforward fully connected neural networks, were tested on the same dataset. The goal was to explore a wide group of statistical and machine learning classifiers to improve the previous classification results even using a much lower dimensional feature vector. The relatively simple linear discriminant classifier provided the best results with an average overall accuracy of 82.93%, together with F1-score values of 78.75%, 96.15%, 80.56% and 77.88% for aubergine/cucumber, melon/watermelon, pepper and tomato, respectively. Very similar values were achieved using the non-parametric classifier based on fully connected and forward propagation neural networks.