Save Subset of MongoDB Collection to Another Collection

I would advise using the aggregation framework:

db.full_set.aggregate([ { $match: { date: "20120105" } }, { $out: "subset" } ])

It works about 100 times faster than forEach at least in my case. This is because the entire aggregation pipeline runs in the mongod process, whereas a solution based on find() and insert() has to send all of the documents from the server to the client and then back. This has a performance penalty, even if the server and client are on the same machine.

Here's the shell version:

db.full_set.find({date:"20120105"}).forEach(function(doc){
   db.subset.insert(doc);
});

Note: As of MongoDB 2.6, the aggregation framework makes it possible to do this faster; see melan's answer for details.