Not exactly. The specific heat of ice is about half of the specific heat of water.

So 6 tonnes of urine at 37°C would take 12 tonnes of ice from -37°C to 0°C.

That's still ice, though, and it takes way more energy to thaw ice that to warm ice from -37 to 0.

Actually, I'll just do the math.

6 Mg piss * 37°C * 4.18 J/g°C = 929 MJ

Let's say ambient ice temp is -20°C.

20°C * 2.05 J/g°C * X + 333.55 J/g * X = 929 MJ

X ~2.5 tonnes of ice melted.

Not too bad. I suspect the change in albedo is the real problem.