What will happen if i accidentally get the eeg electrodes wet in the rain during a prolonged ampulatory study?

This might adversely affect the recording. Check with the clinic that placed the electrodes and they should be able to sort this out for you.

Highly unlikely that the electrodes will be either disconnected or damaged, but it is always best during an ambulatory EEG to contact those folks who set up the study to inform of potential adverse events, as the final reading will need to sort out concerning events vs artifactual events.