If you soak your swollen foot in ice cold water will it help the swelling reduce.?

No. Soaking can cause swelling.
Injury. Only if the swelling is caused by an injury. If the swelling is do to a vascular problem, this soaking can cause critical problems.
Yes but find out why. It would be important to find out what is causing the swelling. We would need to rule out congestive heart failure, kidney disease, venous insufficiency and nutritional issues such as lack of protein in the diet.
Yes. If you are using an ice bath as you suggest make sure not to do it for more than 10 min so tissue damage does not occur.
Ice for swelling. Yes. Icing an injury in the first 72 hours after injury helps reduce swelling. After that it is best to apply heat to enhance the healing process.