Does water from glaciers have many minerals (hard water) or would it be considered pure or distilled water?
Water of glacier origin is at the beginning very close to distilled water.
As it comes into contact to sedimented dust and rocks/minerals in a glacier, or flowing from it, it gets contaminated by solid particles ( glacier rivers are very turbid ) and eventually by some dissolved minerals.
But even then, mineral content is still very low, compared to other water sources.
Consider Earth water cycle as a giant distillation apparatus, contaminating water along all its path from the source to the glacier deposite. These contaminants are solid, liquid or gaseous of both natural and human origin.
For many technical cases, it case be used after filtration insteadof distilled water, similarly as rain water. But for serious lab usage, it is too contaminated with undefined trace contaminants.
My understanding is that the water in glaciers constitutes over 2/3 of the designated 'freshwater' on earth and is an integral part of the so-called water-cycle.
Per U.S. Geological Survey, to quote:
Just because water in an ice cap or glacier is not moving does not mean that it does not have a direct effect on other aspects of the water cycle and the weather...Even though the amount of water locked up in glaciers and ice caps is a small percentage of all water on (and in) the Earth, it represents a large percentage of the world's total freshwater. As these charts and the data table show, the amount of water locked up in ice and snow is only about 1.7 percent of all water on Earth, but the majority of total freshwater on Earth, about 68.7 percent, is held in ice caps and glaciers.
And further on the age of the freshwater itself:
Short-term storage might be days or weeks for water in a lake, but it could be thousands of years for deep groundwater storage or even longer for water at the bottom of an ice cap, such as in Greenland.
As such, the captured freshwater from the atmosphere found in glaciers is apparently representative of especially CO2 and existing pollutant concentrations.
So on the question: "would it be considered pure or distilled water?", that depends on the age of the water and in what region the glacier resides as select places have experienced significant air quality problems.
For example, see this 2019 work: Air Pollution in the Hindu Kush Himalaya, indicating troubling visible signs.