Interesting question, it relates to the heat of fusion of water ice.[1] I think the issue is that there just isn't that much ice on Earth, so its heat capacity (which is somewhat proportional to its temperature) dominates the equation. Here's the information you'd need to do the math yourself:
>"It has been estimated that there are 1,386 million cubic kilometres (333,000,000 cubic miles) of water on Earth.[6] This includes water in liquid and frozen forms in groundwater, oceans, lakes and streams. Saltwater accounts for 97.5% of this amount, whereas fresh water accounts for only 2.5%. Of this fresh water, 68.9% is in the form of ice and permanent snow cover in the Arctic, the Antarctic and mountain glaciers; 30.8% is in the form of fresh groundwater; and only 0.3% of the fresh water on Earth is in easily accessible lakes, reservoirs and river systems."[2]
[1] https://en.wikipedia.org/wiki/Enthalpy_of_fusion
[2] https://en.wikipedia.org/wiki/Hydrosphere#cite_note-Shikloma...