Life is always about balancing risk vs reward, and the answer is different for every person. The risk of an accident is quite low but the accident is not just a minor one it is usually fatal or disfiguring. How do you balance that with the rewards which are guaranteed (fun for the kids and you) but no near as large in scale as the damage from a bad outcome.
For me, I never let my daughters near the farm tractor since it is a hobby farm and there is no benefit to them learning how to use it, and the potential result of an accident was too big for my liking. The lawn tractor was a different story. They loved to ride with me and I would just go slow on the flat areas. Low risk, right? Wrong.
It was all good until one day I rounded the corner of my house and my 4 year old daughter ran straight at me to climb on. I hardly had time to stop the tractor before she was planting her foot on the mower deck while the blade was still spinning, and jumping onto my lap wanting to go for a ride. If she had missed that step by just a little bit, she would have lost half of that foot. That was the last time, because suddenly the risk was much more real to me.
Now if my daughters want me and I am on any tractor, farm or lawn, then they are expected to stay clear and wave their arms to get my attention. Only once I have stopped and signaled to them, are they allowed to approach closer. To me the risk is just too great. I get plenty of time playing with them at other activities, and they get plenty of exercise and time outdoors riding their bikes and playing tag, etc.
Everyone will come to their own decisions, but for me it took only one close call. I am not pushing my (and my children's) luck any further.