Even after reading the book several times, I still can not figure out who he is. My only guess would be that he is a Lan, but I do not recall Lan wearing armor and he definitely did not have two swords.
Lan does wear armor. Here's a quote from Chapter 48 of Eye of the World.
When he came back now, more often than not there were gashes in his armor, bleeding gashes in his flesh, and his warhorse stumbled and bled, too.
And from Chapter 9 of The Great Hunt:
Suddenly Lan was at Rand's stirrup, in his gray-green scaled armor that would make him all but disappear in forest or darkness.
As for the two swords, that's probably just the liberty taken by the illustrator. It's not a big deal, and it looks pretty cool.
The man riding is definitely Lan, although he never wears armor in that part of the book. There are lots of problems with the cover art from the books. On TEOTW, Lan has two swords strapped to his back, Moiraine is riding a pony, Perrin's axe is wrong - it should be a battle axe, and Mat looks about 40. There are problems with many of the covers - a bunch of the early books have hairy men with horns on their helmets that are supposed to be trollocs, for example. The first one that RJ was really happy with was TPOD.
This was referenced in The World of Robert Jordan's The Wheel of Time - there's a chapter that has large prints of all of the covers up to that point, and the title of the chapter is "Some Narrative Paintings of Questionable Authenticity".
If I had to guess, the woman riding would be Moraine, so the natural assumption would be that the knight would be her warder, Lan. Having said that, Lan is never depicted in the books as having worn armor.