Seattle-Copenhagen-Vienna Flights Qs

You won't see your bags until Vienna most likely but you will go through customs in Copenhagen.

You will also have to go through a complete security screening in Copenhagen, so make sure your carry-ons are in compliance with EU rules.

Would three+ hours be enough time to go through customs/immigration in Copenhagen? I'm not sure what all that entails.

Most definitely. Its like the US, you may or may not fill out a form but they check your passports and that's about it. Make sure you follow the signs marked "Connections" or "Transit" for your next flight. I've never been to CPH, but in Rome and London they are very well signed.

The last time I flew through Copenhagen (92), it was Seattle to Copenhagen, then Copenhagen to Frankfurt. At that time, you did not go through customs in Copenhagen when you were connecting to somewhere out of Denmark. In fact, that's why my dad (who then travelled a lot as a flight instructor) preferred connecting in Copenhagen. Check and see if it has changed!

When you make a connection in Europe arriving from the US or elsewhere, you generally not have to retrieve your bags at your connection point. Your bags are almost always transferred to your final destination without your intervenience. There are a few exceptions in some contries if your connection is purely dosmestic, but this is not the case here. When you transfer in Europe the rule is now as follows: you clear immigration (passport control) at your FIRST point of entry to the so called Schengen area, in your case Copenhagen. You clear customs at your final destination, Vienna in your case. The reason for this is logic. The Schengen area is now one immigration zone with no border controls between countries, so travelling between Schengen countries is almost like travelling on a domestic flight. Therefore you need to have cleared immigration before being let into the Schengen part of the airport where your flight to Vienna departs from. Customs is at your final destination which is a necessity in order to allow seamless baggage transfer. You can't go through customs without your baggage in hand. Note that in Vienna you have to use the customs channel saying "arriving from outside EU, nothing to declare", usually the green channel, since your original departure point is the US, not Copenhagen. There is often an extra security checkpoint at your transfer point when arriving from the US.
"Operated by Austrian Airlines" means that your flight is a code share. It's an Austrian Airlines flight which have both an Austrian Arlines (OS 304) and a SAS (SK 9415) flight number.
Minimum connection time in CPH is 45 minutes, and 3 hours is plenty of time for a transfer in CPH. Gate numbers in Copenhagen are usually not displayed until 1 hour before departure.

Thank you so much! I don't know what I'd do without this board!

Flying to the EU is EASY! Customs usually takes half as long as it does in the UK and US. Don't sweat it. You probably don't even have to fill out any paperwork. We didn't when we flew into Paris 3 weeks ago.

Often you go through customs without even noticing it! The booths are very often unmanned.