You can bring infant carseats into restaurants, but in the parks, that would mean bringing the carseats into the parks, which would mean leaving the babies in them most of the day, which isn't really good. A baby that is sitting up can use a high chair, but with younger ones that won't work.
I think that the best strategy is to plan to mostly eat outdoors or at off times while in the parks. In resort restaurants (or at BW or DTD) the carseats will be fine.