American Airlines is having a sale on flights from Austin to a variety of airports in Germany and Switzerland. Fly January to March, mid-week, and you may need to select a stay of at least 7 days.
Here is a list of destinations from Austin, taken from EscapeATX:
The EscapeATX blog post tells how you can find and book these fares, some as low as $515 round-trip.
Of course, the weather will be chilly during these months, but there are some relatively mild days in March. For example, on March 15 the average low temperature in Munich is about 32F with the average high about 48F, with only about a 25% chance of precipitation and 9 mph average wind speed. If you layer your clothing, this is comfortable walking-around weather for most people.