Dan - this is a common and widely held misperception. Because we are saving daylight in the winter, we have more of it to distribute during summer -- well, actually the distribution begins in the spring (when we go on standard time) and goes through fall (when we go back to saving daylight).

The other factor, which doesn't have as great an impact as daylight savings, is that in the summer the sun moves closer to the Earth. Because of this the light from the sun reaches us more quickly -- i.e. - earlier -- thereby making the days longer in the summer.

One other thing to point out is that at extreme latitudes the effect of daylight savings is compounded because the curvature of the earth diminishes near the poles. The DST affect is raised by the latitude exponent. So near the arctic circle, there is almost constant night in the winter, and the opposite in the summer.