There are many ways to carry heat.
The first is conduction, which is about the "vibration" of atoms on one material passing to another by simple physical contact. (Example: you touch something hot and get hurt).
The second is convection: hot molecules simply move from one place to another (Example, water starts to boil in the bottom of a pan, but moves on the top because is lighter).
The third is radiation and is precisely what you say: a warm body emits electromagnetic radiation. At "normal" temperatures (an oven, a human body), it's Infrared radiation, but it can be of higher frequency at higher temperatures, according to Planck's blackbody radiation law.
Notice, though, that the power emitted by radiation only is proportional to the fourth power of temperature. So the effect is very relevant in sun, but negligible for a human body. It should be around 500 W/m$^2$, which OK, is not small, but probably the most heat is transferred by conduction when the human is in air.
This is how garments work: they create a small layer of warm air around your skin, avoiding contact with constantly renewed cold air.