When we go in for lunch, or for a quick warmup, my daughter insists on taking off her boots. Unfortunately, she then wants to either walk around a bit - or head down to the washrooms - which results in wet socks (and colder feet later).
We solved the problem by packing a pair of yurt boots for her to wear in our daypack. These are warm, waterproof, and can squish down to a very small size. Warm and dry socks definitely make for a better afternoon on the mountain!