There's no cutoff age. It depends on the child.
Two things to bear in mind:
Firstly, children have a wide a variety of intellectual and emotional differences. If you're 16-year-old refuses to demonstrate a working knowledge of cold-induced conditions and their symptoms, his opinion is largely irrelevant. Defer to your own opinion as the adult.
But, if your 8-year-old can comprehend and demonstrate a working knowledge of the effects and symptoms of being too cold (e.g., frostbite and hypothermia symptoms), you can trust them to an extent. Just bear in mind, children have a particular high tendency to hyper-focus on their play and fail to notice their bodily signals. You'll often need to pay attention for them.
If your child hasn't yet demonstrated an ability to keep track of their bodily signals (cold hands, blue lips, shivering), you need to be calling the shots -- and probably checking on them with regularity proportional to the coldness.
There's no defined age-cutoff at which a person is suddenly intellectually and emotionally mature enough to understand what "too cold" is. Lots of "adults" get frostbite and hypothermia every winter. And lots of young children manage not to.
Secondly, cold tolerance differs greatly between people. From "how long does it take to get frostbite or hypothermia" (Business Insider):
Surprisingly, hypothermia can occur at any temperature lower than
normal body temperature. Factors like body fat, age, alcohol
consumption, and especially wetness can affect how long hypothermia
takes to strike.
Emphasis is mine.
Whether you feel or don't feel cold can be pretty irrelevant to whether your child is OK. This applies to being too cold and too warm. You really need to keep an eye on the signs and learn your child's tolerances. And, per the first point, you need to be responsible for the monitoring activity until your child demonstrates they're able to.
Anecdotally, my oldest son, can play outside on calm, 40-ish (F) degree days and come back feeling fine, with incredibly warm hands, lips, face, etc.. My oldest daughter, has a higher metabolism and is much leaner and seemingly more muscular. If it's below 60 F., she generally needs to wear a jacket or she'll come back in with freezing hands and blue lips.
But, neither one of them consistently recognize the need for a jacket.