My kitchen sink cold water has frozen 2 times in the past 2 weeks. The hot water did not this time but did the first time. I also have a dishwasher; could that have something to do with it? I can do the work, I just need to know what I can do to stop this.
Try running the hot water to the sink until it's Hot, and then let it run slowly so it stays hot, while leaving the cold open. This will get some heat into the area where both pipes run. As soon as any cold starts to trickle through, switch the faucet to all cold, the cold water passing the ice will gradually melt the blockage.
If you can apply heat to the pipes directly (without burning the house down) that may help - in many cases merely opening the kitchen cabinet under the sink helps, and if you direct stream of hot air at the pipes there it will help more.
Once you get it unfrozen, if you cannot manage insulating the pipes, keep them dripping (a deliberate slow "leak" down the drain) when it's particularly cold, which will help to keep them from freezing again.