It seems to be common knowledge that icing an injury, such as a sprain or a bump, is beneficial to treatment. I'd like to focus this question on sprains (with no bone damage). Does it actually help the body heal or is it just to numb the pain?
Webmd recommends to ice ankle sprains but states "There is not good scientific evidence that ice or contrast baths help, but they are often used."
This NCBI article states that
Randomized controlled trials provide insufficient evidence to determine the effectiveness of rest, ice, compression, and elevation (RICE) therapy for acute ankle sprains in adults. Treatment decisions must be made on an individual basis, carefully weighing the relative risks and benefits of each option, and must be based on expert opinions and guidelines. Sufficiently powered, high-quality, and appropriately reported randomized trials of the different elements of RICE therapy for acute ankle sprains are needed.
This article points out that icing may cause less pain so the person can do there exercises better
In the later, or rehabilitation, phase of recovery the aim changes to restoring normal function. At this stage the effects of ice can enhance other treatments, such as exercise, by reducing pain and muscle spasm. This then allows better movement. If you are doing exercises as part of your treatment, it can be useful to apply an ice pack before exercise. This is so that after the ice pack is removed the area will still be a little numb. The exercises can also be done with the ice pack in place. This reduces pain and makes movement around the injury more comfortable.
I'm a bit confused as it seems like icing an injury is so basic it doesn't need a scientific test to prove it's usefulness. For example there isn't a scientific test that proves bandages are useful.