Tea cozies need very careful use. If placed over a pot of tea that contains tea leaves and hot water, the tea is likely to over brew and taste "steweed" or bitter. It is much better to brew the tea using an infuser, remove the infuser and leaves when the liquor has reached a perfect strength, and then cover the pot with a cozy. Alternatively, strain the infused tea into a second warmed pot and cover with a cozy.
Some teapot manufacturers still make the attractive style of pot that was very popular in the 1930s and 40s - the "Cosiware" pot - which has an infuser that sits neatly in the neck of the pot and lifts out easily, and a fitted jacket of insulated chrome which ensures that the tea keeps beautifully hot.