People worried that cooling a person down too fast by packing on ice or ice-water immersion causing heart attack or that shivering or vasoconstriction might slow cooling should consider that there are situations where people find themselves in ice-water. A well known, and well studied, situation is the effect on survivors of a sinking or aircraft ditching in cold water.

Consider that people who abandon ship and step off into freezing water without protection don't tend to die of heart attacks, nor does vasoconstriction or shivering make much difference. The heat-sink effect of ice-water is so profound that shivering and vasoconstriction don't seem to make much difference on how long you survive.

In fact if vasoconstriction was effective in protecting your core from heat loss there would be no significant advantage to the Heat Escaping Lessening Posture (HELP) where you ball up form fists and tuck your arms in tight. The fact is that the HELP posture works and can significantly increase the time you stay alive in cold water. Which conversely suggests that vasoconstriction isn't very effective.

Of course ice-water immersion is only indicated if the person is at or very near 106F. Lesser cooling methods are entirely acceptable for less drastic situations and heatstroke is always best handled by prevention.

A person drifting into full-on heatstroke represents a massive and protracted failure to take action to control their body temperature. Except in a few rare cases it takes a considerable amount of time to progress to heatstroke. Intervention, by any handy means, at any earlier time will almost always prevent heatstroke. Something as simple as moving a person into the shade, having them rest, and having them sip water can often eliminate the problem before it becomes a medical emergency. Moistening the clothing and fanning can help speed cooling.

But if and when a person crosses the line into heatstroke you need to pull out the biggest guns you have. The biggest and most reliable gun we have for dropping core temperature is ice-water immersion. If you have ice on hand there is no reason to not use it. If there is no ice available use whatever method you can make happen with the materials you have. The goal has to be to drop their core temperature by the most effective means available.