If you are thinking of using lifts and not a free village slope then Ski Amade, Serre Chevalier, Les Arcs and the Skiwelt usually offer free passes for kids at Easter. Lots offer free passes for younger skiers all year round (as DaveP suggests).
To counter Edukator’s opinion (who I know has more experience than I do!) – we’ve been away every Easter for the past 8 years. We’ve never gone mega high, the highest skiing we had at Easter was in Les Arcs and this is also the worst conditions we’ve had (it was an unusually dry and warm spring). Probably the best skiing we’ve had at Easter was staying in a Ski Amade town at 700m.
If you are driving then stick it out, wait and book accommodation somewhere where you know the snow will be fine close to the time. I’ve found that the week leading up to Good Friday is quite busy in the places we’ve been keeping an eye on, but from Easter Saturday they start to get quieter (we are looking at Austria though). Austrian ski areas are geared up for guests arriving by car. Car parks are free and usually right next to the lift.