At least putting the ones I can think of into their houses, first with the characters that tend to stand out more for me, with their reasons:

Rand - Gryffindor - never one to back out of tough situations (except understandably when it puts others into danger), and chivalrous to a fault.

Perrin - Hufflepuff - as per pottermore, hufflepuffs value hard work, patience, loyalty and fair play, which I think covers Perrin well, plus I think the unspoken part of tending to care for animals more, which I think Perrin does as well

Mat - between Gryffindor and Slytherin, at times errs on the self-preservation side of things, and is quite cunning which is more of a Slytherin trait, but at times can be very courageous.

Egwene - Slytherin - like you, I am a fan of Snape, so don't necessarily think of Slytherin as evil, but I think the 'use any means to achieve their ends' covers Egwene quite well

Elayne - Gryffindor - all about bravery / being courageous is Elayne

Nynaeve - between Hufflepuff and Gryffindor, for similar reasons as you outline, but strong on loyalty, fair play, hard work etc. but also very courageous.

Min - Ravenclaw - while at times can be courageous, seems more to think things through, and avoid conflict when possible, as opposed to the charge headlong in I tend to associate with Gryffindor

Aviendha - Gryffindor - very much the charge headlong in side

Ishamael / Moridin - Ravenclaw - all about philosophy / cleverness, which ended up taking him down the dark path, but when not crazy didn't seem to quite fit Slytherin's pattern

Others I will just list against houses, without outlining the reasons at this stage, feel free to query me if differ though:

Moiraine - Gryffindor
Siuan - Slytherin
Elaida - Slytherin
Lan - Gryffindor
Thom - Hufflepuff / Gryffindor
Tam - Hufflepuff / Gryffindor
Elyas - Hufflepuff
Gaul - Gryffindor (most of the Aiel rank and file fall in here I think)
Rhuarc - Hufflepuff
Amys - Hufflepuff (most of the Aiel Wise Ones / Chieftans fall in here I think)
Semirhage - Slytherin / Ravenclaw
Mesaana - Ravenclaw
Moghedian - Slytherin
Asmodean - Ravenclaw
Aginor - Ravenclaw
Demandred - Slytherin / maybe a bit of Gryffindor
Sammael - Slytherin / Gryffindor
Rahvin - Slytherin
Lanfear - Slytherin / Ravenclaw
Balthamal - Slytherin
Graendal - Ravenclaw
Be'lal - Slytherin / Ravenclaw