Winter tires are essential. After seeing 40 winters in Germany, I think driving with summer tires in winter is simply thoughtless, foolish and dangerous. Everybody I know change their car's tires twice a year. I don't understand how rental agencies could even offer the option of summer tires in winter. It's not only snow you have to worry about. Icy roads are frequent, especially in the morning, and much worse than snow.
Besides, there is a new law that states cars need appropriate equipment according to the weather conditions. Meaning that you'll be in real trouble if you have an accident or any other meetings with the police while driving on wintery roads with summer tires.

P.S. Check if the agency's standard tires are summer tires or if they have at least those "M&S" (mud and snow) all year round tires. With the latter you'll get by if you avoid the mountains.