Chester is still excellent in the rain. In Islands, there is sheltered viewing for the tree kangaroos, the Malayan tapirs and the sun bears (plus the binturongs, if they leave their dens) and of course the Monsoon Forest is completely under cover - although it can get crowded, so go early or late if the zoo is busy. The boats on the Lazy River trip have some covering, but you may not see many animals from them if it is raining.
A fortnight ago,I looked at the goats with 2 friends from ZooChat, but none of us knew what breed they are.