I really appreciate stories (we're not talking about gag-a-day or something) where characters are allowed to have a wardrobe and not just. 1 outfit and maybe a jacket (unless there's a good reason, like they got robbed or something)
That being said, characters need to be distinguisheable to me beyond their hairstyle or outfit. Big exception of course if your style is very simplistic like Adventure Time and bases their design on colour and shape a lot, but even AT gave PB and Marceline a very wide-ranging wardrobe and they're still recognizeable.
So yeah, if your characters wear a school uniform, suits or anything that... doesn't really set their personality and then only get distinguisheable due to their whacky hair colour... it's kinda a turn-off to me but doesn't completely ruin it. Colour usually saves it but if you end up with a black/white, it's getting really difficult.
I think what people don't realise is how easy it is to create different-looking characters just with basic shapes like overall face shape, eyes, nose, and eyebrows. If you learn how to draw 4 different kinds of each, you got 4^4 (256!) possible faces from that alone.
- square / round / heart-shaped / angular face shape
- bushy / thin / arched / round eyebrows
- round / tilted / droopey / slim eyes
- pointy / hooked / straight / knubbly nose
and I mean that's just a few options and combinations of the same category are possible too of course, so go wild! This would work for anything little above two dots and a line as face, literally no exception on any styles.
If you are really, really unsure, maybe draw X amount of different face shapes, different pairs of eyes, sets of eyebrows, and noses seperately, make sure they fit into your style and don't take longer than any of the other. Then just play puzzle with them! Kind of like dress-up dolls. I think that might help to get started, and then just make adjustments like where exactly what goes, how sharp the angles are etc.
If you want to make sure you're not suffering from the same face syndrom, I recently stumbled upon the "Babs and Kara" test - essencially, you draw all of your characters in the same bathrobe and their hair covered by the same towel so you have nothing to distract from their face. I found it very fun to draw (and made me crave a spa day) and it really makes it easy to look at the complete face of your characters.