In Germany normally not much thanks to climate change, but the weather is obviously unpredictable. Just 10 minutes of snowfall while you're on the Autobahn (the German highway) can be fatal, if you only have summer tires on your car. Also keep in mind that even though Germany might look small from a US perspective, the terrain is very diverse. So if you drive from London to the Austrian border, you will at least cross a few hilly areas (Siebengebirge, Westerwald, Taunus, Spessart and the Voralpenland) where snowfall may occur while it would just rain in lower-lying regions. As for Austria, most of the country is very hilly or even mountaineous.

Bottom-line: Be prepared and request winter tyres on your rental car. Depending on where you go in Austria, skid chains might be necessary as well.