SoftICE displays diagnostic messages that say:
NTICE: HARD_ERROR ...
These messages are generated anytime the NTRaiseHardError routine is executed. SoftICE simply displays the message that NTRaiseHardError provides, so no, these messages are not generated by SoftICE itself.
Many times these hard errors are handled, and execution continues normally. There are many times when these actually do result in a problem as well. These errors are documented in the ntstatus.h header file in the DDK.