NO, one should not have any cold drink (soft drinks, cold coffee, ice tea, etc) with food.
When a person consumes food, the food is digested in the body by digestive fire in the the stomach. But when we have a cold drink along with food, the digestive fire is suppressed. Thus the food is not digested well inside the body. Due to this, body is not able to turn the food into nutrients and the undigested food lays inside the body and some portion of it is flushed out in the morning.
Harmful effects of Undigested food :
1. Food is not converted into nutrients, thus body (cells) is deprived of nutrients.
2. Undigested food accumulates in the body over a period of time, which leads to many problems such as Indigestion, Joint Pains, lack of energy, etc
3. Undigested food causes acidity, constipation, etc that leads to weak digestion system.
Weak digestion is a primary source of 80% ailments in body. For example, undigested food deposits in various parts of the body and can cause joint pains.
Thus we should avoid having cold drinks while consuming food !