Snowshoeing is great exercise and a fantastic way to see the mountains. It is, basically strapping them on and grabbing a set of poles and off you go (with the correct clothing, map, first aid kit, food and water supplies). You can hire them at most places that hire cross-country ski's and they will advise on the correct size of shoes and height of poles. The poles give you a bit extra balance (especially getting up after falling over

) and a great upper body workout. I would recommend sticking to the marked snowshoe trails that you can find in most ski resorts, as there is always the danger of avalanches if you head off the marked trails into the mountains. Also, try to avoid the cross-country ski trails if you can (or stick to the edge of them),as it does ruin the grooming and frustrate us cross country skiers.
There is plenty of information on the web and you can also check out
www.swisssnowshoe.ch and
www.raquettes.ch
for events in Switzerland. I think Coop or Migros are running a few events over Switzerland this year.
You can start with some training off the snow by doing some walking with poles (also called Nordic Walking). The trick is to actually use the poles when you walk (unlike all the women I see dragging them behind while they are catching up on the weeks gossip

) and add some hills to your walking. There are lots of events you can plan for at the end of the snow season (they normally have a nordic walking event with every major running event here in CH) and it will help you train for your mountain climb.
And lastly, I would recommend giving classic cross-country skiing a go. It is easy on the body and the knees and a great all over workout (you will find muscles that you never thought you had). There are lots of events all over Switzerland (and Europe) that you can aim for (loppet or Swiss loppet series). The Engadine Ski Marathon (42 or 21km classic or skating race through St Moritz) is one of the best races in the world. Its fantastic to see people in their 70's and 80's still getting out there and racing.
Don't worry about the competitiveness of the races. Yes, the Swiss are competitive, but they stay up the front and there are always a few of us down the back having a great time. Its all in the competing and not the competition.
Anyhow - just a few thoughts. Happy training.