How tall does a mountain have to be to have a snow cap?

This will depend on many other variables besides altitude, including latitude, humidity, atmospheric pressure, temperature, solar orientation and historic weather conditions. Snowpack on mountaintops is a dynamic process. Snow that gets melted or blown away must be replaced by new falling snow in order to maintain a constant depth. Glaciers can transport snow, ice and cooler temperatures to lower elevations than would otherwise be snow-covered.

Thanks to oceans currents and convection, the relationship between latitude and temperature at sea level is also complicated.

Let's assume that the average summertime temperature is 42 degrees C at sea level, for some latitude. Dry air temperature drops roughly 3 degrees C per 1,000 feet of altitude. If this were the only factor at work, a mountain at this latitude would need to be higher than 14,000 feet in order to have freezing temperatures year round at its peak.

After a long cold winter, a mountain might retain snow late into the summer. If snows come early the next year, then the contra-solar side of the mountain will have snow on it all year round. Reduce any of these factors and the mountain might have no snow cover the next summer, unless sublimation is negligible and the temperature never goes above freezing.

In the distant arctic and antarctic regions, the ground at sea level is always snow-covered. In contrast, Mt. Kilamanjaro in Africa is an interesting case. Only 3 degrees south of the equator, the mountain is over 19,000 feet high and has been losing snowpack for the past century. Photographic records show the rate of melting. After a snow-covered interval of 11,000 years, this mountain's top will probably become free of ice and snow within the next decade or two.

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