Frost forming in the refrigerator vents can be caused by several things. I referred to your profile and did not find a model or serial for your refrigerator. Without the model and serial number I can only give you general things to check.
Your refrigerator has a defrost system that removes the frost that forms on the evaporator coil while the compressor is running. A defrost timer turns the compressor off every 8-10 hours and turns a heater on. The frost is melted and the water runs through a drain line from the freezer and sometimes into the refrigerator. From the refrigerator another drain line takes it down to the condensate pan underneath the refrigerator where the heat from the compressor evaporates the water. Sometimes the drain runs from the freezer through the back wall and down the back of the refrigerator to the condensate pan.
If there is a problem in the defrost system, the frost will form on the vents in the freezer section. If you have frost there, that might be the problem.
If this drain line stops up water will form in the air diffuser or vent in the rear of the refrigerator and the cold air will freeze it. You can tell if this might be the problem by looking underneath the drawer at the bottom of your refrigerator. If the drain is stopped up there will be water standing underneath the drawer. You might try to unstop the drain line yourself or call for service and have a technician diagnose and repair the problem.
Another thing that can cause the diffuser to freeze over is a leaking door gasket or a door left ajar. Check the gasket by opening the refrigerator door and inspecting it for tears or other damage. Check the gasket seal by putting a dollar bill on the cabinet and closing the door on it. There should be a slight drag as you remove the dollar bill. Move the dollar bill and close the door again until you have gone all the way around the door. If it is leaking air you will find where it is happening.
Check the food in the refrigerator and be sure nothing is sticking out past the front edges of the shelves.
The refrigerator can be repaired unless it is old enough that some parts are unavailable. The question would be is it worth repairing. If you don't find anything simple with the checks I have given you it would probably be worth the expense of having a technician diagnose the problem and give you an estimate for the repairs.