Sleet Storm: do crampons stop you from falling prone?

The 3rd level spell Sleet Storm has the following effect:

The ground in the area is covered with slick ice, making it difficult terrain. When a creature enters the spell’s area for the first time on a turn or starts its turn there, it must make a Dexterity saving throw. On a failed save, it falls prone.

Crampons (price: 2 gp) provide the following benefit:

A crampon is a metal plate with spikes that is strapped to the sole of a boot. A creature wearing crampons can’t fall prone while moving across slippery ice.

Does wearing crampons mean the Sleet Storm spell can’t knock you prone?