I go to that lake many times and had actually been there in November so I can try to help with distance and access. Basically to paint the picture there is a rural type highway, two lane fast moving cars, with lots of turn outs along the way into RV parks, some private drives, etc. Then the entrance to the lake. To get to the lake you simply turn off the main hwy and into the parking lot. When you first pull into the parking lot a hard right takes you to about 6 very simple camping spots. Basically one big open gravel area with parking spaces and fire pits and some wooded space between the hwy and the camping spots. If you are headed to the lake itself you pull around to the other part of the parking lot, it would be the same as moving over one parking isle at a Target, to go park at the trail entrance for the lake. You can not drive onto the lake. In fact you can barely see the lake through the trees from the parking lot. There is a small out house type restroom, a bulletin board with info, and then two trails down. One trail directly to the lake which is indeed narrow flanked by steel poles as mini path guard rails and then another longer more windy totally dirt path to another section of the lake. Both are accessible in the winter but the gravel trail with clear rails is the most used in the winter and leads to a small dock. It would be just wide enough for a snow mobile but definitely not a truck or vehicle.
When I was there in November the parking lot was open and while not officially maintained it was clear enough for a few rough parking spots. The snow packs down in spots people park in a few times over so while it is not smooth it was do able to pull in. Once in you can not see who is in the parking lot from the road and once in the parking lot you can not see who's on the lake well either. If you did have to park out by the locked gate there would be room to park about four cars would be my guess there right in front of the big gate. If you are parked there you would be basically in the entrance to the driveway off of the main hwy so you could see all of the cars parked there while driving by. Im terrible with distance but my best guess at distance would be it's about 1000 ft??? Man I wish I could judge distance better.
It wouldn't be too terrible and if he had a sled it can actually be fairly easy to pull the sleds along packed snow. Ironically the fuller they are often the smoother and easier they are to pull. It also wouldn't be unusual for someone to hop on a snow mobile from their car and ride in. People ride snow mobiles and four wheelers all around that area so no one would think twice if he had a snow mobile zipping around there. They also make snow mobile trailers that carry game, etc. so that is certainly a possibility too.
Even if you can park right at one of the front lake parking spots you are still looking at a little walk down to the lake down the trail. But again snow mobiles are all over that area so that would be an easy way to haul weight out onto the lake. Not a shed, etc. but anything else.
There is another entrance into the lake from what I would call the back side but it would have to be snow machined into that time of the year because its just rolling slopes and fields of snow. The parking area is far away from there, like a mile, and its private land belonging to the university so that would be MUCH harder than parking in the right spot and going down the trail.
Hope that helps. I did post some photos of the trail leading down to the lake earlier to give some perspective.
