Estimate is 13.0 feet height from the base of the keel to the top of the bow pulpit with mast down, assuming the sketch from https://sailboatdata.com/sailboat/catalina-310 is accurate and the bow pulpit is the highest non-removable part of the boat, plus low boy trailer height off grade to the bottom of the keel. Recommend measuring the height from bottom of the keel to the highest non-removable part of the boat yourself to be sure.
Catalina should have the info at their fingertips. They sent me the cradle drawings for my fin keel 310. I shipped our fin keel from TX, so wing shouldn't be a problem. Wish I had pics of boat on the trailer.