I don't know about Mansfield Zoo - but Gorge Wildlife Park was threatened by the Cudlee Creek bushfire in the Adelaide Hills back before Christmas. That fire is now under control and the park has been open most days since - other than catastrophic fire rating days. Sydney Zoo is quite a long way from the national parks and bushland that has been burning. They are on the edge of the Western Sydney Parklands - which is mostly grass with a few areas of bushland - so there is always a threat from local grass fires, but it's very different to fires burning in the mountains and would be quickly brought under control by metropolitan fire services. I'm not aware of any other zoos under immediate threat. Technically, the small Shoalhaven Zoo in Nowra is fairly close to bushland that could flare up again - but it's not currently under threat and they've not posted anything of note on social media or on their website. I've read some comments that the Birdland Animal Park in Batemans Bay was on fire - but can't find any more details. All of the media coverage was about Mogo Zoo and smaller facilities don't get any airtime. On the Perch bird park near Tathra was closed for a few weeks due to the fires, but have posted on Facebook that they were not directly affected and will soon reopen. I can't find anything else that might have been impacted at this point.
In reply to your specific enquiries: Mansfield Zoo: The Mansfield area is threatened by fires to the east in the Alpine National Park. They are in a "community information" zone, which is the lowest threat level of three zones used to advise people as to what to do. The zoo itself is on the western edge of that zone, ie the furthest away from the actual fires. In that regard they should have time to enact their fire plan and hopefully secure their animals. Sydney Zoo is actually located close to the geographic centre of Sydney. If it was threatened by wildfire we would have much bigger problems. On the other hand it is in a park, so there is always the potential for a grass fire, but that would be a local matter. Two zoos that has not been mentioned are On the Perch and Potoroo palace at Tathra on the south coast of New South Wales. Tathra is threatened by fires to the north-west and south, and is about 30km from the nearest fire front.
