There is an exploit that makes it easier as a woman if you marry.
As for tactics, there are many ways to play the game and win. For me, I prefer a mostly cavalry army with 1/3 archers to soften up enemies. Against the Fierdsvain, I will let my archers do as much killing against wave after wave as possible because their infantry is really good against cavalry and other infantry. Against others, softening up and then a charge will do the trick with minimal casualties.
Cavalry has several advantages over infantry. They produce charging damage even if their weapon does not hit. The charging damage cannot be blocked. And the charge staggers the enemy allowing for a strike from another cavalry following behind. The stagger also prevents a counterstrike from the enemy as cavalry rides away to charge again. Cavalry only gets into trouble when bogged down in a group of enemies, but then again, so will your infantry. Cavalry can at least ride away while infantry cannot escape and will be slaughtered by an incoming horde of Huscarls or Beserkers.
Almost certainly you'll want to be a combination of horse archer and knight. You can play an infantry commander for fun, but I don't think that's the most effective. By being mounted, you gain all the advantages of cavalry, the charge bonuses, the couched lance damage, and the ability to move away and pick the spots you want to attack. I use a fine light lance which is quick, can couch, and has decent range of 190 (or is it 185?). I use a shield with that lance. The other two spots are used up by my Ruby Rune Bow and large bag of D'Shar arrows. I find that most shots are one shot kills for me so I don't need Noldor arrows, I need more quantity. I also have another large bag in my inventory which I can reload from if I want, though in tough battles I usually can't find my starting position and don't bother.
Although I have a moderately fast horse of 45, it is a lot easier just to shoot mounted enemies from behind instead of trying to catch up and stab them. Stabbing them takes several hits while my bow is usually an one time kill. I will use lance to couch and stab people on the ground when charging at them.
Yes you will have to invest in power draw and horse archery to become the baddest mounted fighter, but it's well worth it in my opinion. What else are you going to save up your points for, trade? Your companions can do all the spotting and so forth while you can focus on leadership, training (all my companions train), some inventory management and prisoner management. The rest of my points go to abilities that make me a good fighter. There are more than enough skill points available to fully develop power draw and horse archery. I even have enough extra left over in my game that I have 5 persuasion. Again, I don't see what people are using skill points on if not on power draw and horse archery which are two of the biggest difference makers in the game. No matter what, you'll want to develop power draw, even if on foot because of sieges. I am able to kill 100+ enemies on siege defenses due to my ruby rune bow without much if any risk of getting hit. If you do not have power draw, you'll have to go to the front lines and hack away at enemies, which can be more effective (faster kills with swings instead of shots) but you'll also take the risk of being knocked out by some random enemy shot that comes out of nowhere. That's happened plenty of times.