Standing still will make you colder. Move muscles; move blood; move. My guess is that brisk movement is worth about ten, possibly twenty, degrees Fahrenheit. Upward. Get there by walking.
Intense exercise is surprisingly iffy. Doing it for an hour a day, including a warm-up and a warm-down, is usually fabulous for getting in shape. But its value against hypothermia is less, because its heat-production worth probably wears off within the next hour. Low-stress exercise may also be good for physical fitness but offers little for hypothermia after a few minutes.
Instead, to be warm, do continuous exertion all day. Even a little, as long as it’s most of the time. Standing is better than sitting, unless you’re too tired. Movement is very helpful. Walk, at least. The blood going around is worth degrees of warmth. Outside in winter, I walked faster. (Someone who saw me said I did. I believe him.)
I’m not an exercise expert, but I’ll suggest a few: If you sit a lot, press your palms together until you feel your chest tighten, hold a while, release, and repeat. Carry something in your arms or hands instead of rolling it, if it’s 20 to 50 pounds (a common carton of paper is 50 pounds). Take stairs instead of elevators. Walk up escalators. Walk. Exertion that works your chest or thigh muscles are probably best, since those mucles are the most massive and likely do the most to warm your blood. It’s okay to run for winter exercise and not being afraid of freezing while running is doable.
Dressing to be cool temperature-wise probably indirectly helps physical fitness.