Both my sons greatly enjoyed a ride on the mower with me. They didn't get a ride until they were 3 or 4 years old, however.
Kept my arm wrapped around their waist and even let them steer.
There has to be a line drawn somewhere between being safe at all cost, and actually enjoying life. I understand safety, but you have to be a real moron to run over a kid that you're holding in your lap.
Just my opinion of course.