As you get higher it gets colder. If you get high enough it gets cold enough for the snow to stay.
The snow line.
Only high in the mountains and on glaciers does it remain snow covered.
Lots of mountains have snow all the year round. The mountain just has to be high enough that the average temperature is below 0°C most of the year, and the few days in summer which are above 0°C are not enough to melt all the snow which fell during the long winter. Examples are the Himalayes, the Andes, the Alps etc.
Antarctica. And a country is canada
While Mount Fuji does have snow on its peak for a significant portion of the year, especially during the colder months, it does not have snow all year round. The snow typically remains on the summit from about October to around early June.
Some examples of European mountains that are covered in snow year-round are the Alps in Switzerland and the Pyrenees in Andorra. These mountains have high elevations and cold temperatures, which contribute to their perpetual snow cover.
Yes, there are many glaciers on the mountain above about 8,000 feet where snow and ice don't melt. Hundreds of inches fall every year on Paradise Ranger station which is around 5500 feet, and it often doesn't completely melt until late June or July at that elevation. But it does all melt. You have to get above 7-8 thousand feet, depending on the year, to find snow that does not melt.
No. Australia's Snowy Mountains, in Kosciuszko National Park, do not have snow all year around. Snowfalls usually begin in late May, with the June long weekend (Queen's birthday holiday) regarded as the start of the official snow season. Snow continues through to September and October.
No, to have snow on top (permanently) the height of the mountain must exceed that of the snow line for the particular latitude at which the mountain is located (the snow line is higher at the equator than it is at the poles). Mountains that do not reach this height are not permanently snow capped (they may have snow on in winter months).
Yes, there are numerous glaciers on the mountain, which means there is snow and ice year-round. If you plan on visiting, there is typically still snow on the ground at Paradise during much of July, though this depends on the year. All roads are open in July, however.
Many of the National Parks have high mountains with snow throughout the year. I visited The Rocky Mountain National Park and roads were closed in June because of heavy snow fall. The Grand Tetons National Park is another with high peaks.
Yes. And the permanent snow fields are sometimes called glaciers. The altitude is high enough -- making the temperature permanently below freezing -- so that whatever moisture is in the air falls or collects as snow or ice crystals.