Things like that are where translation gets tricky. While we could say "how deep is the snow" in English, it would be far more natural to ask how high it is. Cases like this are when we have to abandon a literal translation and instead go with a cultural one.

I'm glad you are enjoying the original Japanese. I think most people don't care but I always post it for people like you who do care. As a haiku reader myself I know always want to see the original whenever I read a translation.