Current text classification approaches usually focus on the content to be classified. Contextual aspects (both linguistic and extra-linguistic) are usually neglected, even in tasks based on online discussions. Still in many cases the multi-party and multi-turn nature of the context from which these elements are selected can be fruitfully exploited. In this work, we propose a series of experiments on a large dataset for stance detection in English, in which we evaluate the contribution of different types of contextual information, i.e. linguistic, structural and temporal, by feeding them as natural language input into a transformer-based model. We also experiment with different amounts of training data and analyse the topology of local discussion networks in a privacy-compliant way. Results show that structural information can be highly beneficial to text classification but only under certain circumstances (e.g. depending on the amount of training data and on discussion chain complexity). Indeed, we show that contextual information on smaller datasets from other classification tasks does not yield significant improvements. Our framework, based on local discussion networks, allows the integration of structural information while minimising user profiling, thus preserving their privacy.