Watching too many Chinese movies about "Kung Phooy" might give the wrong idea about combat "magic".
Here is a story about "combat". I have a friend who is a fourth Dan black belt in Karate. He told me many years ago that Karate is more a way of life than actually fighting, but of course it is very successful in defence! Except for one thing, he has said many times to youngsters learning Martial arts.
"Absolutely nothing is a defence against a perfectly delivered, unexpected, straight Left!"
Well I wouldn't go as far to say that there's not this is an opinionated question and as such the same for the answers personally i believe there is such thing sense you can enchant objects with spells rite? and for the more gifted and talent.. the idea of super heating the air ans super cooling it wouldn't be so hard to do so such as the idea of wizard fire or or wizard ice wouldn't be that hard of an idea to see happening... I mean after all if you warping energy and weave it into something wouldn't you or couldn't you make something like that happen?
There is an old Sufi technique called the power punch of Moses actually but it takes a while to learn. Sufi rituals usually involve sitting for long hours chanting verses from the Koran. Practicaly speaking however, if someone tries to mug you, there's very little magically you can do except to pray to whatever deity you believe in. If you mean as in can two people who are angry at each other start cursing each other with foot track magic, and what not, then yes but it's unlikely.
For ages soldiers have carried items to help protect them in battle. Many times shields were not only made of wood or metal but also adorned with symbols to aid in their protection. More modern soldiers carry a lucky charm in their helmet. This might not be the flashy combat magic that some are seeking but these are still considered combat magic.
As for how the magic is used some people actually can just hold out there hands and make the other person suffocate with pressure... not sure if this is magic of the type or just hold ing and launching energy.... or just effecting the aggressors psyche...