I think it's because as you get higher into the atmosphere it get colder so when mountains get snowed on it just usually sticks cause its not hot enough to melt the ice or snow so it remains cold. Nice quiz though! And congrats on your 4,700th quiz!
Piggybacking off of this to say that the snowline is also heavily dependent on the amount of snowfall. So tropical snowlines tend to be lower than subtropical snowlines because the tropics are wet, and get a ton of precipitation. You can get further down the mountain before the amount of snow that falls cannot keep up with the melting. You can get glaciers down to 16,000 feet in places like New Guinea or equatorial Africa, while the colder northern Andes of Chile, right next to the Atacama desert, can have snowlines above 20,000 feet even if those locations are colder. In the drier Atacama, the little snow that falls on the cold summits often just sublimates away before it can build up an ice sheet. glaciation is really dependent on a combination of temperature and snowfall, so long as there is more snow falling than snow melting, glaciers or ice caps will form.
What about Heard Island (ref https://www.ga.gov.au/scientific-topics/national-location-information/dimensions/remote-offshore-territories/heard-and-mcdonald-islands), an Australian external territory? Should that merit a mention similar to how DK is mentioned?
https://www.jetpunk.com/user-quizzes/1744710/paises-con-mayor-superficie-cubierta-por-hielo