What about the Jinete (Genitor) or Lancero (Lancer), I think they really are the most spanish unit, this is why:
- 500 years of history, from 14th to 19th century.
- They are influenced by the Andalusian cavalry, included the use of the iconic Adarga shield (still on use by the Soldaros de Cuera on American Southwest at 19th century).
- Had action on the Reconquista, Colonial Conquest and European campaigns.
- Are the origin of the Gauchos, Llaneros, Charros and Vaqueros (Cowboys).
- The spanish horsemanship is directly related to the bullfighthing tradition.
- Jinetes were actually the most usefull and significative unit on the (apart of the thousands of native allies) of Conquistadores.
So on game they could still have the Conquistador related bonus but with a broader representation of spanish cavalry tradition, both on time and regions.
Not that they are a bad choice but they are personally to me not as iconic as the tercio or the conquistador. That being said considering the abundance of unique cavalry units with horses used in the game I think that Spain could easily get something else and leave horse based units to other civs.
Like you said they were inspired by the Andalusian Cavalry and were the origins of Gauchos, Llaneros etc. which could also be used by a multitude of other civs already.
That being said there's also no reason why conquistadors couldn't be depicted riding on horses, considering the Spanish were the ones who brought horses to the new world and it could reflect that.
It is because "American Exceptionalism"

Well actually I would be happy if America is again either the only playable anglocolonial nation or even better the only colonial at all, if that open place for others civs. I think Americans have a way bigger impact on the world history compared to what could add Canada or Australia.
I can not bring again how absurd is to hear about the "canadian civilization", if Firaxis want a civ about artic forest, trade and peace deals why not simply use the native people that actually were part of all these. Also Austalia like a frontier colonization civ? Hello there is the best example of frontier colonization and it name is AMERICA.
Seriously Canada and Australia are kind of autonomous parts of the UK with very recent and administrative independence.
Well that was in response to making Australia and Canada as separate "colony" civs in the game, which to me wouldn't work if you still have America as a playable civ, which what I was referring to.
Eh I personally don't have a problem with Australia because geographically it is separate from all the others, and it's one of my favorites to play as.
I don't actually have as great an opinion on Canada. I can take them or leave them. I'd prefer the former because I think you can introduce more interesting civs from that geographical region, which we know is true because of the Cree.
Also I'm pretty sure they kind of passed off Canada as not anglophone in the game, but francophone considering Wilfred Laurier as the leader can speak French as well. That being said I'd rather Haiti if we get another francophone civilization for Civ 7
That being said I don't want the game to be over saturated with colonial civs but if we get America, Australia and Haiti along with Brazil returning and Argentina, for a Spanish speaking one, I'd be fine.