Just now I saw an elderly person walking unsteadily on an icy pavement near me. I felt they should have remained indoors but even more alarming is they had their hands in their pockets. If you slip your arms can help you keep your balance and if you do fall an arm injury is preferable to a head injury. Falls are a primary cause of injuries resulting in death in older people. This is even more relevant if you are on blood thinners as a fall could result in a bleed in the brain!
Remember hands out of pockets and walk like a penguin in icy conditions.