The joys of coloured cups is that no one knows what is in them so the older ones can have water and the baby can have milk. I would offer it to him mid morning outside. Are you giving the baby a chance to have a morning nap if he was used to doing that at home which I know probably coincides with being outside. Realize that outside is totally knew to him as he won't remember grass from last summer if he even actually got down onto it or was in a sitter, on a mat etc. A blanket and some of his usual house toys that are easily washed will help him make the connection that it is the same place. He may even take to a playpen outside as his preferred place.