Yup.
Adrenaline response is multifaceted... Physical as well as mental. What you're talking about is a side effect of blood being yanked to your core (brain & heart), which is one of the physical aspects. Means in a fight? You won't bleed out. Well, you could, but it would take awhile. Anything on your skin's surface may not even bleed, but even deep slashes or bites on your arms, legs, and even abdomen? Just won't affect you that much. The body sends just enough blood to your extremities to keep them functional, and limits blood flow in general.
You may notice a skin pricking feeling, just before it happens, or start sweating...and then brrrrr. Exactly like a fever, that initial sweat makes you feel cold, which is part of the trigger to pull your blood to your core.
Hot flashes & flop sweats are also part of this when you're cycling / your body is trying to regulate its systems in ongoing anxiety. More commonly, your mouth will be dry, your skin dry, your vision narrowed, hearing acute, and c-c-c-cold.
A sudden dump of adrenaline, meanwhile, is often described as "ice water in your veins". It really does feel cold when your sympathetic nervous system kicks on.
