There is a vast number of places to ski in eastern Europe. Mostly the large ski resorts are well advertised, but many lesser known locations with ski slopes get very little publicity and yet these offer superb value for money facilities for family skiing holidays.
There is little point in paying huge sums for ski passes and accommodation when children are learning to ski. You may as well go to a cheaper destination and pay local ski tuition fees, practise on beginner slopes until everyone reaches a high standard. Then go to the best slopes where one can ski for miles and take advantage of more challenging runs.
Eastern Europe offers many cheap skiing resorts. The south of Poland and Slovakia, for example are very popular with Russians who ski there every year. Why not take a look at the chalets, apartments and log cabins on offer, and skiing opportunities in Eastern Europe for yourself.