The "rate of change" is proportional to the difference in the temperature between the glasses of water and their environment (Newton's Law of Cooling).

This means that the colder glass is changing temperature faster (it's rate of change is larger because its difference is larger).

Think of it like two balls rolling down a hill, where one ball is starting further back but is also steeper.

The ball on the steeper hill will be going faster... but that is no guarantee it will get to the end of the hill faster, because it started further back.

Depending on the exact setup, you could either have the ball on the steeper hill gain enough extra speed to make up for the extra distance it has to travel and win the race. Or it could also lose the race because it started too fast back for the extra speed to be enough.

tl;dr the ice water will be "cooling" faster (the temperature change will be more rapid"). But will it "finish" cooling to room temperature faster? Maybe... need more math.