So basically:
Turns 1-10 (or until you get HBR from a village)
1 worker on beakers
1 worker on hammers
Explore and find villages with GP
Then, after getting HBR) all workers on Hammers and rush horses as quickly as possible
Try to get first horseman up to veteran before making army.
Correct?
no, not at all.
4000BC Settle your city. Put two workers on science to research HBR. Explore with your GP. Look for huts and land that you can name.
3500BC You have completed reasearching HBR. Now put two workers on forests, start producing horsemen. You usually can have close to 40 gold by this point, from your GP exploring. Rush the horsemen with gold whenever you can.
After you get the first horseman, go look for more barbs and huts. Gold should be quick to come by since the horses can get to the barbs quickly. After you get 3 horses, form the army, whether they are vet or not. A horsearmy overruns barbs, so it's easy to upgrade them at that point.
Typcially by 3000BC, you can have your first horsearmy. If you get one early enough, it's often a good idea to produce a second and sometimes 3rd and 4th army, depending on how much gold you get, whether or not you are being rushed, and how effective a subsequent horsearmy would be vs. teching up immediately.
What I listed above is generally for GAs, GHs,and GLs.
With a scientist: set workers on 2 forests in 4000BC, set it to produce a wonder or galley, and then explore with your GS to get huts. Return him to your cap by 3500BC, or earlier if you have picked up gold. Once he's back to the cap, use the Scientist for HBR, and switch production to horsemen, which you should get the first one for 0 gold because you have banked 20 hammers by 3500BC.
With a Great Explorer (gold): 4000BC, set workers to research HBR, Use the GE for 50gold, rush a warrior in 4000BC, and another in 3900BC. Go find barbs and huts. You should have plenty of gold to rush horsemen by 3500BC.
With a Builder: Set workers to 2 science, research HBR. Set production to a Galley, use the Great Builder to rush the galley. Go into the city screen, it will say "Gally next turn" and "rush for 0 gold". Don't rush the galley for 0 gold. Instead, at this point, switch your building order to produce warriors. It will then say "Rush Warrior (X3), 0 gold". Do this, and you have 3 warriors on the first turn. This is the most powerful start, and you'll have no problem getting early gold, and maybe an early warrior rush as well.
This is the fastest horserush. The Aztecs are the second fastest usually. The Chinese are the other fast ones that can reliable horserush (the russians and indians can also horserush faster than most other civs, but only in specific cases).