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Ummm, no.
The transition phase of any substance, in this case, the transition of liquid H2O to solid H2O, involves removing molecular energy from the substance (i.e. heat). If a substance starts with more heat energy, it naturally will take longer to remove that energy than an equal mass of the same substance with less heat energy given an equal cooling rate.
This can be easily shown by the fact that both substances will have a given amount A of heat energy to radiate while the second substance will have A + B amounts to radiate.
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