How do I secure wooden balusters to an exterior stair railing?
Toenailing through the baluster on the uphill side with a finishing nail gun should be quite sufficient. The plowed channel holds them laterally. If you wanted extra strength, you could add glue just before nailing. 

16 or 18 gauge nails about 1 inch to 1 1/4 long should suffice. The hole will likely be nearly invisible.

Additionally, plowed railings usually come with a filler strip that is angle cut to sit between the balusters after they are attached.  If you use the nailing gun (and glue if you wish) to attach those as well, they would further lock in the baluster.