Personally not a fan of horseman rushes, but that's partially because I play exclusively with random tech tree atm on Deity. I oftenndont know when I can expect to get horsemen up, but usually it's a lot later than rushing them with the standard tech tree. The same goes for swordsmen/men at arms.
For both random and standard tech tree however, I am a big fan of a warrior-based rush into swordsmen with battering ram support. Especially on random, doing a warrior rush off of 2-3 cities while looking for battering ram and swordsman tech have been giving me some decent results. The drawback is of course that random tech tree can screw you over if you dont unlock craftsmanship and political philosophy early, or battering rams and swordsmen follow diverging paths unlocked by a bunch of senseless techs that give you no immediate benefits. The benefit on random is that warriors are at least consistent in that you can always build them regardless of bad tech luck, even though they fall off hard compared to a standard horseman rush where the tech tree is known. Therefore the window of opportunity is also (usually) smaller on random.
In the end though, rushes like these are indeed a "gambit" (to use chess terms), in that you are putting your eggs in one basket and hoping to develop quickly enough to exploit a weakness in order to secure a favourable middle game.
Like Victoria, I do not recommend a pure archer rush on anything above Emperor. Mixed as support for other units (esp warriors/swordsmen), sure, but not as the main force.