This paper studies the dynamics of opinion formation and polarization in social media. We investigate whether users stance concerning contentious subjects is influenced by the online discussions they are exposed to and interactions with users supporting different stances. We set up a series of predictive exercises based on machine learning models. Users are described using several posting activities features capturing their overall activity levels, posting success, the reactions their posts attract from users of different stances, and the types of discussions in which they engage. Given the user description at present, the purpose is to predict their stance in the future. Using a dataset of Brexit discussions on the Reddit platform, we show that the activity features regularly outperform the textual baseline, confirming the link between exposure to discussion and opinion. We find that the most informative features relate to the stance composition of the discussion in which users prefer to engage.