Yes, I've done what you would like to do, several times, to Sion direct from a muddy UK field, in Feb and March, in an RV-7. Its a lovely trip. Don't be put off by going in winter. You do need to be thorough with forecasts and give yourself spare time, if things change, tho I have yet been weather delayed. Try to get your IMC rating anyhow. Sion is easy to navigate VMC even if there is a cloud base. The runway is only 1600 asl in the valley floor. Head over Lausanne, next to Lake Geneva, follow the lake into a wide valley straight ahead for a few miles and then follow the same wide valley around to the left, Sion is dead ahead. You are within the mountains for ten minutes at the most. Interesting busy airport, both civilian and military and not too pricey to park for a few days
Train to Verbier, change at Martigny. I once had a door to door race with a friend who was travelling on an Airbus via Geneva, Central London to Verbier. My flight time was a smidge over three hrs and I was quickest total journey time by an hour.
I would wait until you have a bit more foreign travelling hours, a trip or two to northern France, but good luck and watch the forecasts like a hawk.