I’m forever mixing up Ginini and Gingera personally
You're not the only one - for years the wikipedia page for Mt Ginini had the top of Mt Gingera as the primary picture...
Mt Franklin is indeed a good destination for a snow hunt, it's the usual winter locked gate and if it's closed below that (like today) it's usually because there's ok snow further down the hills. The walk up to the trig point gives a bit more height and a view too. Pity the old chalet burnt down as that sounds like a place that would have been interesting to check out.
It's a trig point, one of many around the country which were originally used for surveying purposes. They're basically a vestigal structure now as things like GPS have made them redundant for modern use. This design is pretty common but you do find a few variations on the theme - basically all I've seen have the top circles on a post but the support structure varies.
If you check out prominent hills in your area there's a good chance that you'll find some trig points, they were very widespread and large numbers are still around albeit often in a state of disrepair or with vegetation blocking them from view