You do not need to wear body armor, but a leather or denim jacket may offer some protection against a knife attack, as long as it is loose enough for you to move freely. Thin long sleeves do not offer any protection and are a liability because they are more easily grabbed and held than a bare arm would be. There are some fashionable, slash resistant garments, such as jackets and gloves, which may be worn to offer some protection against knives.
Weather often affects your choice of clothing. In hot, humid weather, it is not practical to wear coats or other heavy clothing that may protect you in an attack. Cold weather may give you more choices for proactive clothing, but extremely cold weather may demand clothing that is too heavy and restrictive for self-defense. However, in this case, it probably means the attacker will probably also be wearing heavy clothing that may slow the attack.
Wearing your martial arts school tee shirt or a tee shirt that advertises your martial art is not being inconspicuous. It lets the bad guy know he will need to be more careful when accosting you, and it may mean that he starts the confrontation with club to your head instead of just demanding your money.