Based on fur texture and face shape, that calf is at least six months old, probably older. Calves can survive without actual cow milk even at three months, though older is better (calves weaned that early are usually fed a sort of formula for another couple months).
Also, nose tags like that one don’t go through the cow’s septum. They basically work like those fake septum rings for humans.
In addition to weaning the calves, another use for nose tags is protecting non-lactating cows. Sometimes weanlings or even adult cows will suck on themselves or other non-lactating cows; this can cause internal teat scarring bad enough to prevent that teat or teats from ever working. I’ve seen this happen, and it’s ugly, probably at least somewhat painful, and, if bad enough, would lead to the cow being slaughtered at a very young age because she can’t produce milk, has chronic mastitis, and/or can’t be milked with automatic milking equipment. So, nose tags actually prevent animal cruelty.
Also, calves will suck on anything remotely oblong (and attempt to eat literally anything), even if they are being adequately fed or overfed. Often they will suck on other calves’ ears, and, since ears are longer than teats and cows have upper as well as lower teeth in the back of their mouths, many calves get bites on their ears, which often become severely infected. I’m not sure if nose tags would work there, because physics—a non-toxic but bad-tasting ear paint would be better—but yeah, letting a calf put anything it wants in its mouth is not always a good idea.