In general your model should make use off al the information in the observed data. It sounds like you are mixing concerns of parameter inference and forecasting, which you could do by fitting a smaller dataset and assessing coverage on the remaining dataset.
But other than that, there’s no reason why you wouldn’t use all the observed past and future information when doing parameter inference.
Overfitting in a bayesian context would be addressed by stronger regularizing priors or different model structures, not by ignoring existing data.