It was a rough night for the first eaglet born at Duke Farms this year, as the eagle chick had to deal with an ice storm its first night alive. The chick was born at 1:30 p.m. on Thursday, after a full day of trying to break out of its shell. Just several hours later, an ice storm pummeled New Jersey, making for a long first night for mom and baby. All of this was caught on the farm’s Eagle Cam, which has livestreamed the Hillsborough nest since 2008. “Mom’s umbrella was up and doing all she could do to keep her newly hatched chick and last egg warm and dry in the icy rain this morning,” Eagle…