There is not really a set season/ month that places are open or closed. Some places are open on limited days / schedules during the slower times of the year. Other places will be closed for refurbs or major changes. Some places are nearly always open.
Places that seem to be subject to limited hours tend to be walk up/ counter service places that arent in the heart of the park. The further out you get, the less likely they'll be open. So, places like the hungry bear might be closed on a quieter day.
Places thare are likely to be open, unless they are being refurbed would be Plaza Inn, Blue Bayou, Riverbell- they are all in the heart of the park.