You'd do it exactly the same as if the file *would* fit on your disk:

local $/ = "\n"; # just in case its been undeffed - don't wanna slurp 
+a TB file!
open(my $fh, "/mnt/remotehost/bigfile") || die("Can't open: $!\n");
while(my $line = <$fh>) {
  ... do stuff ...
}
close($fh);
[download]

Hope that helps!