Best time of year to visit Switzerland

What are your interests and why are you visiting? Skiing or hiking. A little more info would help.

Skiing and other winter sports - December to March.
Hiking and mountain fresh air - May to September
Visiting cities - anytime.

We are considering either September or May. We plan to visit some of the medieval villages and castles, plus do some moderate hiking. Also have a friend in Basel who we will visit. Our interests are history, photography, and medieval sites

First week in May. No question. Been to Gimmelwald twice in the past 3 years and the RS Tour in 2015 got us to the Lauterbrunnen Valley May 2. Had snowed the day before and it was very fairy tale you can think of.

Also was there on a RS My Way tour in Sept 2016 and while great for hiking, the amount of snow was very low compared to May 2015.

Is the first week of October a bad time? To Icey, cold, snowy? I'm hoping we will be able to do some non technical hikes / trails in the Berner Oberland area without any issues from weather.

I've been in late May, early June and mid June. Next year we're going in mid July. We have run into snow on trails all of those times. If you are only interested in Moderate hiking I would recommend any time in June or September.

Is the first week of October a bad time? To Icey, cold, snowy?

We have been in early and mid-October with good weather. In fact, near perfect. I think in 20 nights over the course of two trips in 2015 and 2016 spent in Zermatt and Lauterbrunnen, we had rain 2 or 3 partial days and woke to newly fallen snow on the ridges with bright morning sun one day. It can be chilly though, especially early morning and high elevations. Layers, gloves, hats required.

OTOH we had snow in early September in Mürren once.

We were there in Sept. last year and it was about 65 degrees everywhere, including the mid-point of the Berner Oberland (Murren). I didn't even need an outer layer on the top of Schilthorn (but did for Jungfraujoch). We thought the weather was perfect -- visited Lausanne, Berner Oberland and Lucerne for about nine days.

Hey, Doug!
We went to Switzerland in summer 2016 with my boyfriend. We spent quite some time trying to find the best time to visit Switzerland and chose last week of June–first week of July based on the sources like rove.me, myswissalps, and Rough Guides. 

Our main decision points were hiking season, not too crowded towns and sights, nice weather, and accessibility of major natural attractions like lakes and waterfalls. We enjoyed our trip a lot, especially the Rhine Falls and cheese farms! Hope you have amazing trip too :)