It could be true but then, for your region and for a special reason. I fly a tiny aircraft, summer and winter, here in Norway. I know very well where the cloud ceiling is and, in my region, there is no apparent reason for it to be different with the seasons. But it can be and here is how:
Warm air rises and cools down by the adiabatic effect of a lesser pressure aloft. The average is 0.65 C per 100 meters. If the clouds are lower, it simply means that the air comes faster to the dew point temperature, i.e. the temperature at which the excess of moisture must condense as tiny droplets.
For example, in the morning, the earth and air right above the surface is still cold from the night. The relative humidity is high. The air doesn't have to rise much to condense. The clouds are generally lower in the morning than in the afternoon.
At another place, a warm sea current brings warm water near a very cold and high coast. Very soon, that moist air will "smoke" over the sea. The clouds will be extremely low. The opposite can also be true; a very cold sea current brings cold water along a warm coast. It creates an inversion; warmer air above colder one. Then you get fog, which is simply clouds at ground altitude.
If your observation is that the clouds are higher during the winter then you should try to find out why by looking at your region, its geography, proximity of large body of water, altitude, etc. But there isn't a general reason to have - worldwide - higher clouds in the winter.
EDITED: What Niqueo writes is in fact this: At the equator, the tropopause (the top of the troposphere) is nearly twice as high as at the poles (about 18 km vs. 10 km at the poles). The reason is a combination of the air being warmer, hence less dense at the equator, and the fact that the earth spins and does it the fastest at the equator.
The result is that the international convention to call clouds as being high, varies with the latitude. But ... was that your question?
High clouds will form between 10,000 and 25,000 ft (3,000 and 8,000 m) in the polar regions, 16,500 and 40,000 ft (5,000 and 12,000 m) in the temperate regions and 20,000 and 60,000 ft (6,000 and 18,000 m) in the tropical region