I'm not good at this but let me still have a try.
Cloaks aren't meant as a disguise. From Wikipedia:
"A cloak is a type of loose garment that is worn over indoor clothing and serves the same purpose as an overcoat—it protects the wearer from the cold, rain or wind for example, or it may form part of a fashionable outfit or uniform. Cloaks are as old as human history; there has nearly always been some form of long outer garment used to protect people from the weather. Over time cloaks have changed their look to match current styles and textile needs.
Cloaks generally fasten at the neck or over the shoulder, vary in length, from ankle all the way up to the hip, mid-calf being the normal length. They may have an attached hood, and may cover and fasten down the front, in which case they have holes or slits for the hands to pass through. However, cloaks are almost always sleeveless."This means that according to weather you might see many and even the majority of the people in cities and on the roads wearing cloaks. My char as an example wears a
travelling cloak which serves the purpose to protect her from the cold in the mornings too because she's more often on the roads than in the warm comfort of a soft bed. And this lifestyle is reflected in her garments covered with dust.
If you still need to see what a normal cloak covers, take a look at these. Didn't have time to search for better panels.
http://www.onemanga.com/Vinland_Saga/30/10/http://www.onemanga.com/Vinland_Saga/20/18-19/http://www.onemanga.com/Vinland_Saga/22/07/My char rarely wears her hood up but she almost always has her cloak (cold mornings suck without proper clothes, you see...).
I like the idea of changing the clothes you normally equip on your char when you are disguised. I still ended up meeting Allola when she was wearing a helmet=disguise and saying "cool helmet" though. People will need some time to learn and get used to shady characters disguising in such a way. Of course, you should wear a disguise with some characteristic threads to allow being recognized. It can be fun to roleplay that too

. Being chased is one of the highlights of being a baddy

. Considering a victim will most likely be startled when attacked and therefore not being able to notice and remember all details from the attackers outside appearance, I think Marqsaynt's suggestion can be pretty useful (dice rolling thingy).
Oh, and btw a disguise are not always just clothes or any other material stuff.