The typical usermode dumps or minidumps do not contain enough information to do so. While they contain all usermode memory, they do not contain kernel memory, so open handles to kernel resources like files or network sockets will not be included in the dump (and even if they were, the hard disk has most likely changed so just trying to write to the hard disk may corrupt your system even more).
The only way I see to restore a memory dump is restoring the full memory and all other state like hard disk state, which can be done with most virtual machine software (which will, however, disconnect all your network connections on restore; gratefully most programs can handle lost network connectsions better than lost file handles).