I don't even think it makes sense, since your skin senses it.

It makes sense when you learn that your skin doesn't sense ambient temperature at all, but rather it senses the rate at which you are losing or gaining body heat. This is why metal can feel cold at room temperature while something like a blanket actually feels room temp, it's a better heat conductor so it absorbs body heat from you faster.

Having more body mass means you produce more body heat at any given time, so the rate at which you lose body heat to the air is decreased, making you warmer.