I have seen a lot of times in temples that priests offer milk to snake idols.
What is the reason behind it? Do snakes really drink milk?
There are many folk tale behind the drinking of the milk, the famous one is :-;
A tale of a farmer living in a village. He had two sons and one of whom killed three snakes during ploughing operations. The mother of the snake took revenge on the same night by biting the farmer, his wife and two children and they all died. Next day the farmer’s only surviving daughter, distraught and grieved by the death of her parents and brothers, pleaded before the mother snake with an offering of a bowl of milk and requested for forgiveness and to restore the life of her parents and brothers. Pleased with this offering the snake pardoned them and restored the farmer and his family to life
Coming to your second question which says "Do snakes really drink milk?" and the answer is Snakes don't drink milk
Now I know people over here go and make the snake drink milk on Nag Panchami but the fact is that snakes don't drink the milk. Even if they do, they are not able to digest it and eventually they die.
Milk is for mammals and not reptiles. What the snakes charmers do is that they don't provide food and water to snakes for a day or two before the Nag Panchami, and hence, inorder to quench the thirst and hunger, snakes drink the milk and they die later.
So I ain't sure if anyone still believes that the snakes really drink but I would suggest not to do so, you are taking someones life.
If you truly want to worship Nag Deva (Snake god) than pour milk and offer your food to idols and not the real snakes.
Varaha Purana suggests to bathe the images of Naga in milk on Naga Panchami and it doesn't mention anything about feeding milk to snakes.
- If one remains austere on that day, give us all that is sour in food and bathes the images of Nagas in milk, they become friendly towards him.
Nagas were sent to Patala on Panchama tithi and people celebrate that tithi as Naga Panchami.
Snakes which are present now on Earth do not drink milk but i'm not sure about divine snakes such as Adisesha (serpent on which Lord Vishnu sleeps) and Vasuki (Lord Shiva's snake).