Do they have certain animals out during certain times? Or are they only closed during a certain time of the year

Yes, some animals especially the babies are only out during certain times. There will be signs, if they are

There are certain timea for the rhinos each day. They are not out all day.

For the most part all animals are available for viewing all year, however, Their website does update when exhibits are closed or certain animals are unavailable.

I am not sure about either of these, I do know that animals were removed from their exhibits when we were there due to needing medical treatment but signs informed us that they would be back.