In reply to Cobbler:
Yes, Icebreaker are fantastic, Smartwool also good.
For synthetics - Patagonia, Odlo, Mountain Molehill (US kids brand - 5 is about the top, though).
Polarn o Pyret do both synthetics or merino.
The expensive brands above are pretty reliable in their sizing; there are plenty of cheaper ski brands (Mountain warehouse, Dare2Be, etc) but sizing can be a bit hit and miss, so I'd only buy them with child to compare against/if able to easily return. They're not nearly so efficient if they don't fit well! As a result, I tend to buy decent ones off eBay - and they've generally still been in a state to hand on after both my kids have worn them.