Seeing as how I have my OED out this morning:
Dragoon: 1. Cavalryman (orig. mounted infantryman armed with carbine); rough, fierce fellow; variety of pigeons.
Assuming that the RCDs have no affinity for birdseed, and not knowing enough of them to debate their temperament, I am going to stick with the notion that a Dragoon as a mounted infantryman with a carbine is probably why the Americans (at least that Death Ground fellow) has started to refer to the Guys in the Back of the Bradleys (infantrymen with carbines) as Dragoons.
In Britain when military needs changed roving infanteers that were given horses to allow them to cow large numbers of Scots, Borderers and Irishmen were reroled. They morphed and became part of the Cavalry establishment. At various times they have concentrated on fighting from a mounted position for the assault and at other times the vehicle has been nothing more than transport and they have fought on their feet like line infantry. By the time the Royal Canadian Dragoons took their name the Dragoons in the British Army were cavalry, spending as much time with the sword as the rifle. Peculiarly, in Canada and South Africa the Dragoons were required as Mounted Rifles or Mounted Infantry - the Lee-Enfield was the weapon and the horse was just a vehicle.
But on one point JSG, Franko and I all agree. An Infanteer is an Infanteer no matter what they ride into battle in.
Cavalry fight mounted. Infantry fight on foot. If specialisation is necessary when an Infanteer is mounted in an armoured vehicle (a shorter rifle is required for example) then perhaps that justifies call them something else other than Infantrymen, or perhaps like paratroopers, marines, commandos, riflemen, fusiliers etc they are just another species of infanteer, infanteers that are optimised for cavalry cooperation but infanteers all the same.
If Canada's army was split according to its Regimental titles it would have:
One mounted recce unit - Lord Strathcona's Horse (Royal Canadians)
One armoured support unit - 12 Regiment Blinde Canadien / 12th Canadian Armoured Regiment
One mounted infantry unit (cavalry cooperation) - Royal Canadian Dragoons
3 Light Infantry Battalions - Princess Patricia's Canadian Light Infantry
6 Infantry Battalions - Royal Canadian Regiment, Royal 22nd Regiment
On consideration that is not an unbalanced force. Now all that has to be dealt with is regimental pride, geographic dispersion and national politics.
Cheers.