That is correct - on certain water bodies they are not allowed. For example Massabesic lake in Manchester, NH they are not allowed because it is a water supply. However, you can use a sled out there. Weird rule, but anyways.
Squam and winni you can use 4 wheelers. Keep in mind though they must be registered in NH to use in NH. NH F&G patrol this out on the lakes regularly.
I'm sure there are good reasons for all the screwy fishing, 4 whellers etc., rules, they sure can confuse a person. I just try and make sure I know the rule to the letter for the body of eater I fish, which is Squam 95% of the time.