I live in Saratoga Springs, about an hour south of Lake George, and know the area reasonably well.
Lake George is not totally dead in the winter - there is a winter festival (weather permitting), and a few of the shops remain open. But its definitely far more relaxed in the winter than it is in the summer. Frankly, IMHO, Lake George is a bit of a tourist trap.
There are lots of places to visit and explore in the area. Lake Luzerne is not far away - sleepy little town at the confluence of the Hudson and Sacandaga Rivers. There is a fabulous ice cream shop (Papa's), and if you walk next door to the public library you can find a path down the hill to the Hudson River. Doesn't look at all like it does in NYC - rapids breaking over rocks, etc. The lake itself is scenic, and there is a summer camp for kids who have a serious interest in music that offers a excellent summer concert series.
I like to drive north out of Lake George along Route 9N through Bolton Landing, Hague, and on to Ticonderoga. Be advised that other than the Sagamore, there is very little open along this road in the winter. The (reconstructed) Fort Ticonderoga is a destination in Ticonderoga, but be advised that they don't allow tripods. There is also a nice cemetery just south of Ticonderoga (Valley View Cemetery). Further north, at Crown Point, are the ruins of an actual fort that dates back to pre-revolutionary war days. It's now a state park - there's a $6/car admission fee in the summer, but in the winter I suspect that you could just walk in.
You can follow the Adirondack Northway, aka I-87 north to the intersection with Rt. 78, and then work your way over through Keene Valley to Lake Placid, home of two Olympic Winter Games (most recently, 1980). Lake Placid is active year round. A bit further along the same road is Saranac Lake, a slightly large community.
The Adirondack Park is an area of extremely controlled development - one of the current major concerns is that there is a long stretch along I-87 where there is no cell phone coverage, and several people have died after encountering problems in this area and have been unable to call for help. The state wants to correct the problem, but the agency that has authority over the park refuses to approve construction of cell phone towers.
The Adirondack Park is very primitive and is wonderful for camping, mountain climbing, hiking, etc, but there is very little commercial activity and unless you own a "camp", or know someone who does, you probably will have to pay a small fortune to find lodging. The one "big town" (that that is a very relative term) is Blue Mountain Lake, home of the Adirondack Museum. The museum is worth a visit.