I want to illustrate a little further the point that Bev made about reins being just another safety issue when you live in a pedestrian environment (which we all should agree that WDW certainly is.)
My older siblings were all born in the UK. One day late in 1944, Mom was walking along a very busy, very steep street in Leeds, which is an industrial city in the north of England. She was on her way to go stand in line for her rationed groceries, this being WW2. She had my older sister, who was 3, walking on reins, and my brother, who was 9 months, in a pram.
As she started to step off the curb to cross the street (Coal Hill Lane, for anyone who knows Leeds), she slipped and broke her leg, and also hit her head on the way down and knocked herself unconscious. My sister was safe because her reins were looped around Mom's wrist, but my brother was not so lucky. She lost her grip on the pram and it careened wildly into the street. By some miracle, none of the vehicles hit the pram, and someone finally managed to stop it nearly a quarter-mile away. However, it could not be connected to my mother, and when she woke up she was frantic because her baby was missing. He was taken to a hospital by the police, where my father managed to find him late that evening.
By the time I came along some years later, after they emigrated to the US, it was evident that my mother had learned a lesson from that incident. Even in a stroller, I wore reins, and the strap was looped around the stroller handle AND my mother's wrist. She wasn't taking any chances.
Last week at Universal, I fell down a set of steps while leaving a restaurant, and yes, I bumped my head and lost my grip on my son's hand. My DS is 6, but if he had been 2? You bet he would have been wearing reins, firmly looped around my wrist.