But then they'd spend more energy (and more braking) hauling that ice around; would the amount of heat absorbed be more than the one ice train would generate?

There's probably more efficient materials to use, big lumps of supercooled metal. Someone else mentioned liquid air, that could just be evaporated in the tunnels and stations.

Of course, generating liquid air costs a lot of energy too. I'm sure the problem is easily solved if you assume infinite and free energy.