E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A carriage, especially such as a phäeton, dog-cart, commercial sulky, and such like. It is not applied to a gentlemans close carriage. Contraction of trappings (whatever is put on, furniture for horses, decorations, etc.).
The trap in question was a carriage which the Major had bought for six pounds sterling.Thackeray: Vanity Fair, chap. lxvii.
Traps. Luggage, as Leave your traps at the station, I must look after my traps, etc. (See above.)
The traps were packed up as quickly as possible, land the party drove away.Daily Telegraph.