ROME — Nicholas Alexander had a huge smile on his face when he wheeled up to cut a yellow ribbon Tuesday afternoon at the entrance of a playground named for him at Pine Tree Camp. When the ribbon dropped to the ground after a couple of snips, a cheer rose from the 100 or so campers, parents and counselors who’d gathered for the event. The crowd was there to celebrate the opening of Nicholas’ Playground, a barrier-free play area for children with disabilities.