Using aggregate is the right approach, but you need to $unwind the list array before applying the $match so that you can filter individual elements and then use $group to put it back together:
db.test.aggregate([
{ $match: {_id: ObjectId("512e28984815cbfcb21646a7")}},
{ $unwind: '$list'},
{ $match: {'list.a': {$gt: 3}}},
{ $group: {_id: '$_id', list: {$push: '$list.a'}}}
])
outputs:
{
"result": [
{
"_id": ObjectId("512e28984815cbfcb21646a7"),
"list": [
4,
5
]
}
],
"ok": 1
}
MongoDB 3.2 Update
Starting with the 3.2 release, you can use the new $filter aggregation operator to do this more efficiently by only including the list elements you want during a $project:
db.test.aggregate([
{ $match: {_id: ObjectId("512e28984815cbfcb21646a7")}},
{ $project: {
list: {$filter: {
input: '$list',
as: 'item',
cond: {$gt: ['$$item.a', 3]}
}}
}}
])