Could I drink full fat milk on a diet?

Sure. if trying to lose weight, eat the things you enjoy, but eat less. Whole milk is not necessarily a restriction. Of course, the question becomes HOW MUCH> don't want more than 20-30% of your calories from fat in a day. So if on a 1500 calorie diet- 300 calories from fat ( each 8ounces of milk has about 80 calories from fat). Try not to have more than 4 glasses a day. Best to you and weight loss.