There's definitely some good exploring to be had in Hakone (Hakone Yumoto, Moto Hakone, Sekisho no Ato, the Fujiya Hotel, etc.). The problem with Hakone in winter is that travel can be exceedingly difficult when it snows. In March of a few years back, we had to make an impromptu plan B when snow made the roads to our scheduled hotel impassable...which might be difficult for someone to do if they don't speak the language.

So while I'd recommend Hakone in general, it might be better to pick a safer alternative if you have family in tow.