The National Archives magazine, Prologue, ran in 2000 a two-part article on White House Easter egg rolls through the various presidential administrations. I’m attaching below links to both articles, and blurbs about our friends the Roosevelts.
Theodore Roosevelt "could not resist the temptation to witness the frolic of the little men and women. He came out on the southern porch of the White House and remained for a time, a pleased spectator."(56) "The President watched the youngsters [often with his own children] with more than ordinary interest and with a seeming desire to join them in the sport."(57) A younger egg roller, observing Archie and Quentin Roosevelt in 1906, when assured that these were indeed the sons of the President, tugged his father's sleeve and "in a drawling tone said: 'Pop, them uns look jest like we uns.'"(58)
Had Edith Roosevelt had her way, the event would have been discontinued. "It seems such needless destruction of the lovely grass." "Almost worse was the game called 'picking egg,' when pairs of children pecked their respective eggs together to see whose cracked first. The huge number of broken eggs gave off a combined odor that could be smelled three squares away."(63)