Without seeing and knowing more, it's kind of difficult to answer this one,however,pipes can be insulated fairly inexpensively and/or you may be able to temper (add warm water) to some of your cold lines,bringing the water in them closer to room temperature.I'd find a plumber or HVAC person to give you more options.

Matches is correct... The warm humid air in the house is condensing on the cooler pipes and tank. It's like a glass of Ice water, that when you fill it with colder water, the warm humid air will condense on the outside. Insulation is the most inexpensive way to stop this problem. Pipe insulation should be tight around the pipe, No gaps whatsoever.

Will there be any problem with condensation in the studs where insulation will not fit?

Karen