I think the British were the only country that had Light Dragoons. All other countries Dragoons were heavy
HOWEVER - French Dragoons fought on foot very often in The Peninsular.
"During the decades before Napoleonic Wars only the dragoons were trained in infantry and cavalry duties. General Jomini wrote: "Opinions will be always divided as to those amphibious animals called dragoons. It is certainly an advantage to have several battalions of mounted infantry, who can anticipate an enemy at a defile, or scour a wood; but to make cavalry out of foot soldiers is very difficult. ...
It has been said that the greatest inconvenience resulting from the use of dragoons consists in the fact of being obliged at one moment to make them believe infantry squares cannot resist their charges, and the next moment that a foot soldier is superior to any horseman... But it cannot be denied, however, that great advantages might result to the general who could rapidly move up 10,000 infantrymen on horseback to a decisive point ..."
AND FROM
www.napoleonguide.com
(rather than list a long line of books)
France's dragoons were the mainstay of the mounted arm of the forces and were capable of either scouting, or being involved in battle-winning charges. As well as straight heavy-cavalry sabres, dragoons had pistols and short carbines and these allowed them to dismount and fight on foot as highly mobile infantry. This advantage saw them used widely in the anti-guerrilla warfare in the Peninsular War, as well as on independent roles on the army's flanks.