Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from St. Louis to Arlanda as you normally would.
Due to multiple factors, expect to potentially pay more when booking in May. For low rates, March can be a great choice for travel to Arlanda. Flights to Arlanda from St. Louis in March are about $1,005 on average during March, but can be found for as low as $553.