You've not actually linked to where the CDC reports those statistics, so I'm not doubting the CDC so much as I'm doubting your memory of the statistics. The closest I could find from the CDC was that among those 65 or older "about 37% of those who fall reported an injury that required medical treatment or restricted their activity for at least one day"

That's a bit more nuanced than what you said, and isn't limited to slipping on ice (which may be safer, on account of all the extra layers you're wearing).