Will it harm my cedar and white pine trees to cut off several feet?
It would be helpful to know the botanical name of the cedar tree as there are several types. White pines in general grow to about 50-80 feet in height by 20-40 feet in spread. Unless it's dead or damaged, evergreens are best left alone to grow naturally. Large evergreen trees do not respond well to topping.
The removal of the upper main stem through topping opens the tree to internal decay, disease, or damaging insects; it also removes the most productive portion of the crown of the tree. The result is that the tree becomes a hazard to itself, neighboring trees, and your property. If the tree is too large to fit the space, it may need to be removed and replaced with a smaller species.
White pines can be susceptible to sweeping winds and branches can be lost in strong storms.
At this point, you may want to contact several certified arborists regarding the health and pruning of your trees, and the best way to proceed http://www.treesaregood.org/