Are the original UGGs water/weather proof?

My niece needs new winter boots this year so we're getting her a pair for her birthday. While she's here we were browsing online she picked the original UGG style by EMU. I thought I would just get her UGGs then.

Anyway, are the original UGGs water / weather proof?

Can she step in a wet puddle of snow mush repeatedly and not get her feet wet?