[{"_id":"ID","array":[{"a":"A","b":"B","c":{"x":true,"y":true,"z":false}},{"a":"A","b":"B"},{"a":"A","b":"B","c":{"s":true}}]}]

db.collection.aggregate([{$match:{}},{$project:{array:{$map:{input:"$array",as:"arr",in:{a:"$$arr.a",b:"$$arr.b",c:{$size:{$filter:{input:{$objectToArray:{$ifNull:["$$arr.c",{}]}},cond:{$eq:["$$this.v",true]}}}}}}}}}])