Guild-independent urban cavalry:

[Maklodes]

I'm not sure if anyone will find this useful, but I decided to look through what cavalry is available that is 1) recruited from cities, and 2) not recruited from a guild, such as merchant cavalry militia or knights hospitaller.

This is basically to figure out what is good for recruiting a horse breeder's guild. It's possible to get a guild other ways, such as recruiting guild cavalry (like merchant cavalry militia), then destroying the guild once you're confident you have enough points from the horse breeder's guild, or recruiting castle cavalry and building stables and then converting it to a city, but guild-independent urban cavalry is a somewhat simpler path.

Byzantium: Byzantium never gets guild-independent urban cavalry. (To add insult to injury, their merchant's guild cavalry is probably the worst in the game, and they don't get Catholic order knights (of course).)

Denmark: Denmark gets norse war clerics from Abbeys built in minor cities and better churches.

Egypt: Egypt gets Arab cavalry from racing tracks in minor cities and adds mamluk archers from sultan's racing tracks in large cities. In addition, racing tracks directly make horse breeders' guilds easier to get.

England: England gets demi-lancers from military academies and royal officers' acadmies in huge cities.

France: France gets French mounted archers from military academies and adds gendarmes with royal officers' academies in huge cities.

The Holy Roman Empire: The Holy Roman Empire never gets guild-independent urban cavalry.

Hungary: Hungary automatically gets hussars from its huge cities.

Milan: Milan gets Italian cavalry militia from militia drill squares or better in large cities, gets broken lances automatically from huge cities, and gets famiglia ducale from mayor's palaces in huge cities.

Moors: Moors get Arab cavalry from racing tracks in minor cities, Granadine jinetes from Sultan's racing tracks in large cities, and automatically get Christian guard from huge cities.

Poland: Like Hungary, Poland automatically gets hussars from huge cities.

Portugal: Portugal gets jinetes from plaza del toro, built in a minor city. In addition, in America, Portugal gets conquistadors from every large town or larger. (Note that while Portugal gets military academies and royal officers' academies, like England, France, and Spain, in Portugal these academies do not enable recruitment of any units.)

Russia: Russia can recruit weak and cheap militia cavalry from militia drill squares in large cities.

Scotland: Scotland never gets guild-independent urban cavalry.

Sicily: Sicily never gets guild-independent urban cavalry. (This is something of a surprise for an Italian faction, but they get halberd militia instead of Italian cavalry militia from militia drill squares, and they don't get broken lances. (They get dismounted broken lances, oddly enough, from citadel armouries.) At least their merchant guilds provide Italian cavalry militia rather than merchant cavalry militia, which is a very significant improvement.)

Spain: Spain gets jinetes from a plaza del toro in minor cities like Portugal. It can also recruit gendarmes from royal officers' academies in huge cities. Spain also recruits conquistadors in all American large towns or larger.

Turks: Turks get turkomans from racing tracks in minor cities and Sipahis from sultan's racing tracks in large cities.

Venice: Venice gets Italian cavalry militia from militia drill squares in large cities. It also gets broken lances automatically from huge cities.

[Aeratus]

You forgot the Turks, but they're basically the same as Egypt (racing tracks).

[Maklodes]

Thanks. I edited the Turks into my original post.

UPDATE: Also, I decided to remove all the coloring of the city sizes except for the smallest city a faction can use for urban cavalry. For instance, only minor cities is colored for moors, not large cities or huge cities.

[Aeratus]

I think this compilation is very useful, because the Horse Breeders HQ guild is a very useful building, as it provides +2 exp for heavy cavalry. The AI will rarely build this building, so it is not feasible to capture one built by the AI.

Another thing to note is that although Denmark can build cavalry from minor cities, it cannot do so as well as the Iberian and Muslims can, because the Norse War Cleric has a very slow replenish rate.

It is interesting how the Horse Breeders Guild was implemented, since cavalry is usually trained in cities, but only cavalry trained in cities count. However, the end result makes sense, because the Iberians and muslims were historically more renown in horse breeding than others at least during the early middle ages.

[... where did it run?]

Now I might be wrong, but as far as I remember Polish don't get Hussars from "huge wall" building, unlike Hungary does.

[Aeratus]

Another useful measure is the replenish rate. This is very important because if the replenish rate is very slow, it'll take a long time to get enough cavalry units to build the horse breeder's guild.

It looks like Moors have by far the quickest route, having a combined replenish rate of 1.4, while racing tracks themselves add guild points. Milan has a combined 1.7 rate, but require quite a lot of buildings and a huge city to maximize this.

Here are the replenish rates:

[All Muslim Factions] Racing Track, minor city: 0.5
[All Muslim Factions] Sultan's race tracks, large city: 0.5 + 0.4 (i.e. two different units)
[Moors] Huge Walls (Christian Guard): 0.5

[Poland/Hungary] Huge Walls (Hussars): 0.5

[Milan/Venice] Huge Walls (Broken Lances): 0.5
[Milan/Venice] Barracks (Cavalry Militia): 0.5 (large city militia drill square), 0.7 (all higher level barracks)
[Milan] Mayor's Palace, huge city (Famiglia Ducale): 0.5

[England] Military Academy, huge city (Demi Lancers): 0.5 (unupgraded), 0.7 (when upgraded to Royal Military Academy)

[France] Military Academy, huge city (French Mounted Archers): 0.7
[France/Spain] Royal Military Academy (+ Gendarmes): 0.7 + 0.7 (Spain only has one horse unit, while France has two)
[Spain/Portugal] Plaza del toro, minor city (Jinetes): 0.5 - a bit slow, but you can get it very early

[Denmark] Chruches (Norse War Clerics): 0.2 (minor city abby), 0.4 (cathedral and huge cathedral)

[Russia] Barracks (Militia Cavalry): 0.5 (large city militia drill square), 0.7 (all higher level barracks)