When I lived in Augsburg, Germany for four years, I did a two day hike up to the top of the Zugspitze, near Garmish, Germany twice.
The first time I did it with my Daughter, who was about 21 years old. We had a guide and stayed in a hutte the one overnight. It was in late June. It didn't snow or sleet at all, but the last portion of the hike was on frozen snow. It was a great hike.
The second time, I did the same hike with my Son, step-Daugher and step-Son, all teens of High School age. The first day the weather was wonderful, but the second day, it started sleeting by early morning. The Guide asked if we wanted to turn around, but we all said no, we want to do it. Well, it sleeted all day, but we did the second day in record time (according to the guide). We were all wet rats at the top (we had gore-tex protection). This was in July.
Not sure where you plan to hike. You said lower-mid elevations. The Zugspitze is the tallest mountain in Germany, something like 12000 feet altitude. We didn't quite reach the top of the mountain, but close. There is a cog train or cable car going down.
Spring or Fall, not sure it is a big difference, but you might hit more frozen ice in the Spring than Fall.