Before you even venture off to the internet in search of the weather, remember that the climate in the White Mountains is unpredictable. And, it is substantially different from the climate anywhere else in New Hampshire or in the region. What WMUR TV gives for a forecast really has little bearing on what you will find on even the low peaks of the Whites. Occasionally, WMUR will give a "Higher Summits" forecast, but that is usually sketchy at best.
Over the years we have come up with a few resources for reliable weather information. You must remember, however, there really is no one stop shopping for information on White Mountain weather. Much of the information that Chris and I get to take with us on hikes we have put together ourselves. It doesn't hurt that I am a closet meteorologist -- always fascinated by the weather, and lucky enough to take a couple of college courses on meteorology and forecasting.
Always check the available forecast before you leave for the Whites, and then be prepared for the unexpected. Good luck.
For local information, we are blessed with the Mount Washington Observatory. A weather monitoring station that has sat on the top of Mount Washington from 1870 to 1892 and then from 1932 until today. This is probably the best source of information about what is happening on the higher summits and has the best forecast information. Their site has a complete listing of all of their various forecasts. They even provide a camera with a live view from the summit. This page is a must read for every hiker or visitor to the White Mountains / Mt. Washington area. Especially the part about the world record wind.
Conway is about the closest town to the southern Whites that gives a forecast (and its actually from Freyburg, ME). You can figure that your actual weather will be somewhere between these conditions and the ones on top of Mt. Washington. Click this button and you'll go to the Weather Channel site and have access to an extended forecast and detailed maps and radar.
If you wish to make your own forecasts, you can obtain information from the following sources, including satellite imagery, radar imagery, weather maps, and forecasts. These are the resources I commonly use (in the order that I use them):