I think it is correct to say that for all medieval Europe time the basic peasant, worker bed was a cold stone floor or at most a mattress made out of straw. I wonder how and on top of what powerful man in medieval Europe rested and slept.
We'd find them to be very short. People slept sitting, not fully laid down as we do nowadays. People were afraid if you would lay down as the dead, you'd be dead soon. I've visited several palaces. Those beds I found to be really short.
The rich would have four poster beds. Partly for privacy (which wasn't an issue back then), but more for warmth. Close the curtains, you would sleep a bit warmer that way.
For that reason box beds were popular, also among the not so rich. Sleeping in (what we would see as) a cabinet kept the sleeper relatively warm.
Cardinal Richelieu was known to receive guests whilst in bed.
My answer is for the very late medieval and renaissance periods. Bedding materials were the same as for ordinary people, but of much higher quality.