I live about a half mile off the lake, outside Sandy Point, and can access the Lake. It is just over 1 1/2 miles from where I access the lake to the boat ramp at the end of Alton Bay. That would make about a two mile walk (on snowshoes) to get to the parking lot.
Once the lake is snow covered, it is almost impossible to just walk out there. As FLL says you will sink in and will become tiring in a very short distance.
With snow shoes or cross country skis, you can go along ok, but distances can be deceiving. We once got out on the lake and started heading out to Echo Point and were walking and walking and walking, and Echo Point seemed to be no closer. It almost had the appearance of us being on a treadmill
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You can also have some very slushy snow next to the ice, which can soak into boots and cause some very wet, cold feet. Bottom line is be careful, stay on snow mobile tracks, dress in layers, and be very careful. Make sure you are on your way back before you start to get tired!