after sitting on the chair for a period of time why do you eventually feel comfortable
The chair starts out colder than your body, and because metal is a good heat conductor, it conducts heat quickly away from your body. That makes it feel cold. It feels comfortable when it is the same temperature as your skin. Other materials don't feel as cold because they don't conduct the heat away from your body as well.
The chair is a good conductor of heat and initially is likely to be cooler than your skin temperature. So, initially heat flows from your skin to heat the chair and you feel 'cold'. After a while the chair warms to your skin temperature and heat flow slows to a negligible amount and you no longer feel 'cold'.
Because the non-metal chair is a better insulator than the metal chair. It discourages heat from flowing out of your body moreso than does background air. The metal chair by contrast encourages heat to flow through it, and moreso than the background air. Except in very hot climates, your human body is hotter than the surroundings. You are accustomed to a typical amount of heat loss out of each area unit of your body, that you consider to be thermally neutral comfort. If that region of your body doesn't get to reject that amount of heat, that region feels warmer. If that region of your body to rejects more than that amount of heat, that region feels colder.
