When (not “if”) you slip on the ice, your feet are going to shift away from you. If your hips are mobile, you have a greater chance of shifting your support into a position where you might be able to avoid falling.
If your hips aren’t mobile, then you have a greater chance of either ripping some important soft tissue in your groin (ouch!), or planting your face into the floor.
This is why everyone should keep their body moving and strong.