In my finished basement a portion of hot & cold water pipes (kitchen faucet) run up an exterior wall (approx. 6 feet), into the ceiling space, and over to the d.h.w. tank. During a cold snap I believe to water in the pipes froze (no water to faucet). After a few days, the water came back, but its running with very low pressure (less than half of normal). What can the problem be?

Low pressure on both hot and cold? If so, I would suggest removing the aerator and see how the pressure is without it. If much better, clean or replace the aerator and you should be all set.

I agree with mgd, the freeze/thaw can break junk loose inside a pipe and it can clog downstrea. Could be caught in the aerator or the mixing valve too.