There's no evidence that can say for sure that cold baths or ice baths burn off calories but I would believe it to be true.
Since when you get into a cold bath your body works to warm you back up and when your body is trying to produce heat to warm your body up then you would lose weight.
Because as your body heats up you burn off calories and then can lose the weight.
However you won't likely lose a lot of weight taking a cold or ice bath but it can probably help.
You also need to change your diet, watch your calorie intake and get some exercise to really lose the weight.
I've lost weight doing the cabbage soup diet and exercising but I never tried to take an ice bath or cold bath although I thought about it.
But I couldn't force myself into any cold water.