I have great water pressure (both hot and cold) in the front of my house (1st floor and 2nd floor bathrooms). In the back of my house (1st floor kitchen and 2nd floor laundry room) the hot water pressure is great but the cold water pressure is very low. I just replaced an old valve on the cold water line to see if that was the problem but the pressure is still low . This is a new problem (about a year) as I've had no pressure problems in the past. Any ideas?
Somewhere between the good pressure and bad pressure there's a partial clog in the cold water line. Finding it will be tedious. You don't mention pipe material, which makes speculating about what it is difficult - if it's only happened in the past year and no work was done about the time it started, you'll just have to hunt. If plumbing work was done about that time, start there. If you happen to have galvanized iron pipe, think hard about total replacement, IMHO.
Possible clogs include - excessive pipe seal tape on threaded joints getting loose in the pipes - lumps of corrosion breaking loose and jamming downstream - could be corrosion from a waterline outside your house - Sand from a well running low... dissolved materials coming out of solution in the pipes, suspended materials settling in the pipes.
My personal most annoying was a soldered copper elbow that was almost, but not quite, full of solder on the inside (and evidently had been for years.) Great pressure for half a second, followed by a trickle. I just disassembled the pipe until I found it, when I finally faced the agony of fixing it.