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My little guy has 2 pairs of these. He calls them his snow welly boots. They're very hard wearing. He's out trekking a couple of miles a day in all kinds of conditions walking the dogs with myself and the wife. They are holding up well.
If you want your kid to wear extra socks or you plan to tuck trousers into the boots I'd probably recommend going a size bigger. But we didn't feel the need to do these things. The lining is super warm and trousers bunching at the top can be tucked in a little bit and still be comfortable.
We're actually going to be buying a few more pairs for when he grows up. He's only 2 at the moment.