No. Animals are not all cold-blooded. Biologists usually talk about ectotherms and endotherms instead of the informal labels “cold-blooded” and “warm-blooded.”
Ectotherms (many reptiles, amphibians, fishes, and invertebrates) get most of their body heat from the environment. Endotherms—chiefly mammals and birds—generate most of their heat through metabolism and can keep a relatively stable internal temperature even when the surroundings change.
So “cold-blooded” is a rough everyday phrase for ectothermy, not a rule that covers every animal. Birds and mammals are classic counterexamples.
Source: Biology LibreTexts, 33.13 Homeostasis – Thermoregulation.