I rode the Alpe Adria route in late April 2015. I got through with some cold rain, but if I'd been a week earlier I would've faced quite a bit of snow. I thought that I might knock it off in about 4 days, but it took me a full week (including a rest day). I highly recommend it. I thought the first day after I entered Italy where the route passes through a lot of disused train tunnels was possible the most fun single day of touring I've done. Take headlights - not all of the tunnels had lighting.
If you want to tack on another nice ride, start at Ulm and follow the Via Julia south of Munich to Salzburg.
Cheers,
James