Austria has great ski schools with English-speaking instructors, and they normally put together groups of all-English-speakers (and separate groups for Dutch, Swedish...).
For your first trip with such young children, I'd highly recommend the Galtenberg Hotel in Alpbach, Austria. It's about a 2-hour transfer from Munich (which the hotel organises, for a fee) and you should be able to get cheap flights to Munich. Booking directly with the hotel works out a LOT cheaper than going through a tour operator - we used to pay less than £1000 per person at February Half Term which is almost impossible if you go somewhere where you need to fly to Salzburg or Innsbruck. Outside school holidays you should be fine.
The Galtenberg is a so-called Kinderhotel with fantastic facilities for the children. Indoor/outdoor pool, I think there is even a waterslide nowadays. They organise ski school from the hotel and take them back for lunch, and the little ones can go straight into kids club (with soft play area, ball pit etc) afterwards - your DC may surprise you, mine did - never wanted to leave kids' club!
The ski resort is small, but works well with young DCs. Ours are older now and we've moved on to somewhere more exciting, but have very fond memories of our holidays in Alpbach :)
There are other hotels in the Kinderhotel chain but I haven't tried any of the others, and found the Galtenberg to be very good value for what they offer.