Strength-wise they're fine, as spearmen have an effective strength of 14 against their 12, and can use defensive bonuses to their advantage.
That's not the entire story though. Say you have a Drill II spear on a hill and a Drill II horseman attacks it. With no promotions, the spear is strength 7 + 7 (100% against mounted) + 1.25 (25% for defending in rough terrain) = strength 15.25 vs strength 12 on the horse. However, when you start adding advantages on either side, the horseman actually starts to overtake the spear in modified strength since the spear's bonuses are a % of 7 and the horse's are a % of 12. So with those drill promotions, you have 7 + 7 (vs. mounted) + 1.25 (rough terrain) + 2.8 (drill I and II) for a total of 18.05 strength. The horse has 12 + 4.8 (drill I and II), for 16.8 strength. That's only a difference of 1.25 strength, which is a smaller difference than if you just compare the spear's vs. mounted strength tot he horseman's - even including the hill defense bonus. Plus, since combat damage is determined by strength ratios, that 7% strength advantage is only half of the 15% advantage that you get from just comparing 14 strength to 12 strength. Add in a Great General on both sides and you get 19.80 strength for the spear and 19.80 for the horse. Which in my opinion is a problem.
Even with just non-promoted spear (I'll just assume on rough terrain) vs. non-promoted horse with a great general on each side, you have a strength ratio of 7 + 7 + 1.25 + 1.75 = 17 for the spear and 12 + 3 = 15 for the horseman. That's just a 12% strength difference for the spear (again, compared to the 15% difference you get just from looking at the numbers on paper). And that's assuming the spearman has favorable terrain conditions.
Anyways, point of that is that as you add more and more modifiers, a unit that counters another by having such a large modifier starts to fall behind quickly.
The other problem with just looking at the 14 vs. 12 ratio is that it doesn't take into account the synergy between partial victories (i.e. the units don't usually die in one round of combat) and move-after-attack abilities. Whichever party initiates the combat, both will probably be at about half health, and the horseman will likely just move away, leaving a colleague to mop up the damaged and relatively sluggish spearman while the horse heals. So even though the spearman will almost always will eek out a slight strength advantage assuming favorable terrain and promotion/general parity, spears will almost never actually counter 12-strength horsemen. Reducing the movement to 3 would help that, but I don't think that's quite enough.
Man I hope I did that math right.
[edit]Oh right, no I never use horsemen. I suppose I could move up to deity if I did since I've never lost emperor and do really well on immortal, but I'd rather not.