The 'date' command runs in a child process for which the bash shell has
to determine the environment. Parameter assignments are inherited in
that environment (i.e. the 'date' command sees them) in two cases:
either when the variable is not only declared but also exported or when
the assignment is provided on the command line right before the command
itself. From the man page:
The environment for any simple command or function may
be augmented temporarily by prefixing it with parameter
assignments, as described above in PARAMETERS. These assignment
statements affect only the environment seen by that command.
For more information you may want to read the "Command execution
environment" section in the Bash man page.