Henrys law states that P=Kx where P is the partial pressure of  gas above the solution. K is Henrys law constant. K increases as temperature increases. x is the mole fraction of  gas in the solution. According to Henry's law carbonation increases in a solution as temperature decreases.
Since carbonation is the process of giving compounds like carbonic acid (liq) from CO  (gas) {i.e. making liquid from gasses} thus the partial pressure of CO  has to decrease or the mole fraction of CO in solution has to increase {P/x  = K} and both these two conditions support increase in carbonation.