Often, July weather is hot and very humid. Maybe not as unbearable as Washington DC in the summer, but close. Bring a filter and drink frequently from streams during your approach.
Now, once you hit treeline and the wind and clouds set in, temperature can drop into the 40s, so bring wind and rain gear, a hat and gloves, and don't ignore the forecast.
Do not "just throw a tent in the woods" at the base of Huntington ravine - the east side of Mt Washington is crowded and heavily patrolled, and camping is not permitted except in the designated spots.
See http://www.summitpost.org/presidential- ... #chapter_9
andhttp://www.summitpost.org/white-mountai ... #chapter_3
There's no equivalent to Roaring Brook, but Dolly Copp is just up the road:http://www.fs.usda.gov/recarea/whitemou ... 3&actid=29