I had been thinking the same way, so I had a look at the link below the etching. Although the website states the etching was made in 1845 it does not indicate when the portrait was painted. Quote from NRO below.
Quote:
Date 1845
Notes This engraving shows the Rev.Edmund Nelson, father to Lord Horatio Nelson. Edmund was the rector of the parish church of All Saints, Burnham Thorpe in Norfolk. He and his wife Catherine raised a family of eight children at the parsonage, of which Horatio was the middle son of five boys and three girls. This portrait was etched by W.C.Edwards in 1845 and published by C.Muskett of Norwich.