Carp do not have a stomach but a long intestinal tract which takes in food, digests it to extract and absorb energy and nutrients, and then expels the remaining waste as feces.
They are cold blooded and the ambient temperature of the surrounding water affects their metabolism, so when the water is cold, so are they. This slows down their metabolism to the point where they will lie on the bottom motionless for long periods.
When it's cold they need very little in the way of food but also because of the low temperature any food taken in will take longer to digest.
The water in most lakes will be clear at this time of year but even if it's not they can still detect a single boilie from some distance.
Using large amounts of bait will be counter-productive as you will literally fill them up, which will obviously affect results.
Given these facts it is wise to use singles and sticks and an easily digestible bait.
Fish Meals and oils should be avoided in low temperatures as it will affect the emulsification process, they work best in higher temperatures (late spring) also it should be pointed out they are not good for the carp in low temperatures either.
Low protein bird food based mixes (no nuts because of the oil content) are good as is any Carbohydrate based bait with a good attractor/label.
Milk proteins also work well but again you have to be very careful how much you introduce because of the high digestibility and the high protein content.
All waters differ depending on size, location stock etc so you will of course find your own way, but these few guidelines are a good place to start.