Another possibility for hua instead of flower (花) is ” 華”
The root image is similar, the moment of “flowering” (you can see all the crosses in the ideogram as the hua tree in bloom), but it also has the nuance of being beautiful/illustrious or “related to China”.
Actually, it’s more probably 華 than 花. It’s rather rare to have hua (花) in your name – I personally don’t know of anyone with that character. It’s a but too simplistic a term for “flower” – people are generally more specific. For example, my grandmother is 少蘭, “young orchid”.
On the other hand, if they knew they were planning to give the kid a name that was easy for foreigners…
“Bin” also has the possibility of ”彬” – “of literary talent and simple style”
Seriously though, we have so many homophones in Chinese it’s really really difficult if you don’t know the character. So “snow flower” could be a good guess as any.