In reply to wbo:
If it's cold and you're carrying them then an all on one is the way to go.
For our oldest we use a mixture of things depending on the forecast. A simple all in one waterproof suit (Sprayway Newt suit) has been very good when worn over the top of other things if it's wet. For cold but dry, we have been using some of the children's ski suits from Decathlon (but not sure if they still do them?).
For our youngest we have just got an all in one fleece suit and Regatta fleece lined waterproof suit from Go Outdoors. It has been fine for warmth, but we've not got him out in anything really wet yet to see what it's like.
As someone else has said it can be hands/feet that get coldest so a couple of pairs of socks/gloves and, if we know the youngest isn't going to be out walking much, we'll sometime use 'big socks' as an over the the shoes insulation layer (can be taken off if he gets out and walks).
Gavin