When we feel “cold”, what we’re actually perceiving is “getting colder” rather than “being cold”. Same thing with warmth.
The best example I can think of to illustrate this is if you run freezing cold hands under room temperature water, it’ll feel hot, not because the water is hot, but because your hands will be rapidly warming up.
Metal loves to share heat, it’s an inherent property to a lot of metals that it really wants to be the same temperature of the things around it (this is referred to as having high thermal conductivity). So when you touch it, it’s at room temperature and your body is at, well, body temperature (which will be warmer), so you heat it up slightly, but that means it’s sapping heat from you
You feel this cooling down effect which is perceived as feeling cold
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