index.js

var mongoose = require('mongoose');
mongoose.connect('localhost', 'testing_535');
console.error('mongoose version', mongoose.version);

var OID = mongoose.Types.ObjectId;

var ASchema = new mongoose.Schema({
    square: mongoose.Schema.ObjectId
  , task: Number
});

var A = mongoose.model('A', ASchema);

mongoose.connection.on('open', function () {
  var id = new OID;
  A.create(
      { square: id, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }
    , { square: new OID, task: 1 }, function (err) {
    if (err) return console.error(err.stack||err);
    A.find({}, function (err, docs) {
      if (err) return console.error(err.stack||err);
      console.error(docs);
      console.error('next');
      var ids = id.toString();
      A.find({ square: ids }, function (err, docs) {
        if (err) return console.error(err.stack||err);
        console.error('found by id');
        console.error(docs);
        mongoose.connection.db.dropDatabase(function () {
          mongoose.connection.close();
        });
      });
    });
  })
});

When I execute this I get the options logged:

A.find({ square: 'hi' }, function (err, docs) { console.log(docs); });
{ options: { populate: {} },
safe: undefined,
_conditions: {},
op: 'find',
model: { [Function: model] modelName: 'A' } }
[]
A.find({ }, function (err, docs) { console.log(docs); });
{ options: { populate: {} },
safe: undefined,
_conditions: {},
op: 'find',
model: { [Function: model] modelName: 'A' } }
[]