Strictly speaking a cape - a full length cape would be a cloak.
The Elizabethans had very strict rules on what kind of cloak you could wear for your rank, the difference between one trimmed with fox and wolf fur for instance.
I suppose the small ones were to let everyone know you were the 2nd son of an Earl (and had better get a good table) without melting in summer.
It also suggests that Elizabethan Maitre-d's had to be very good at mammal taxonomy!