Lolski - The three years old thing is an average - some kids are stronger/better balanced/more physically coordinated (not to mention able to concentrate and/or follow instructions) earlier than others - I've known 6 year olds who aren't ready for it, and two year olds who are.
And anyway it depends very much upon what you mean by "skiing at three". For extended periods, then they will get tired easily when they're small, so you probably wouldn't want to put them straight into a lesson of an hour or more younger than that (hence very few ski schools will take them even at three). But a little sliding, for a few minutes at a time is fine - what you're really doing is introduce them to the feel of standing and balancing on a moving ski, and having extra long feet which can get tangled up if they're not careful(!), not asking them to really do anything physically demanding. Just let them guide you and don't push it if they get tired.
NBG - Bulgaria may be marginal for snow in December, and most of the resorts don't to be honest have a lot to attract experienced skiers like the rest of your group.
Andorra has lots of British instructors, so you wouldn't have a language problem there. Also it's a duty free country (although it's not as cheap as it was) so prices are lower than in a lot of the Alps, and there are some good shopping opportunities if you find as a first-timer that you also need to spend some time on non-skiing activities. In the last few years they've built lots of new lifts, and joined the various ski areas in Andorra together, so there would be plenty for the rest of your group too. Of the options in Andorra, Pas de La Casa is French speaking, most of the rest is Spanish, but English is widely spoken.
For the resorts served by Turin, you will probably need to find childcare offered by your tour operator if you want it to be English language based, and you'll also not find many British instructors working in Italy (the main exception is if you have a look at the company Interski , who run their own ski-school - tip ask for their brochure now, and they'll offer you an early booking discount for next season, and don't forget that their prices include lift passes and insurance which most others don't).