No hot water in second floor bathroom sink and bathtub/shower, cold water is fine. Pipe is probably frozen but goes up outside wall that isn't accessible without tearing down inside wall. Doubt if it will it help to use heater or hair dryer under the sink, any other suggestions?
We've been in this house for 35 years and have never had a problem before no matter how cold the winters were.

First, open the hot water faucet and then go to the basement and use a hair dryer to heat the pipe. Here, I have assumed that your pipes are copper and in this case the copper pipe will conduct the heat from the hair dryer to the frozen area. Keeping the faucet open is the real trick... if you don't open the hot side of the faucet the pipes will never thaw!

Heating the pipe from up top will also help, so if possible, use another person and heater or hair dryer up top while you work the bottom.

If your pipe has frozen and burst you will need to shut off the main water supply to the house, so be sure to know where the water meter or the main water shutoff is.

Let me know how you make out, OK?

Mark

Mark covered this well. You should keep the cold line dribbling for now, it could also freeze tonight. What material are your supply pipes, copper or galvanized? You can apply a propane torch to a safe section of that cold line. As it dribbles it will be pulling up warmer water and that can give the frozedn pipe a bit of an edge.