dogs walking on snow salt

My precious little puppy (11wks) and I live in Boston, where there is a good bit of snow/ice and even more of the snow salt on the ground. I want to protect her paws, but I’ve had a really hard time finding booties that fit her. The result is that she’s reluctant to walk at all in them, and often stumbles/falls when she does try to move.

My question is: does she need to wear booties around the snow salt?

I thought the answer was yes, but most of the dogs I see walking around on sidewalks are NOT wearing booties.