Well the Victorians are to blame. They covered everything from tables and piano legs to well.....tea cosies!
They made a padded plain cosy for the warmth from old blankets or eiderdowns, and had various covers, so if the cover got dirty or stained they were able to wash them, I think it is a clever idea, one cosy lots of covers. Sometimes the china, tea cloth and napkins would all match.
The tea cosy was probably invented by the Duchess of Bedford who invented afternoon tea, because there was a long time between lunch and dinner. Friends were invited for afternoon tea chatted the tea in the pot would get cold.
You will find these tea cosies here with a few other vintage linens.