Visit www.usa.safekids.org and search under "bike helmet." I just found this there:
"Properly fitted bike helmets could reduce the risk of bike-related brain injuries by 88 percent; however, only one out of five cyclists ages 5 to 14 usually wears a helmet. Each year in the United States, more than 100 children die from bicycle-related injuries, and more than a quarter million are treated in emergency rooms. Nearly half (47 percent) have traumatic brain injuries.
"A bike helmet is essential safety gear. Helmets could prevent an estimated 75 percent of bike-related fatalities and up to 45,000 head injuries to children each year. In many jurisdictions, children under 16 are required by law to wear a helmet at all times while riding a bicycle."
The distance of a fall won't matter. If the child's head hits concrete or anything else hard, even the ground, the damage can be done in even a short fall.
You say you're "a little mad" and you have a right to be. If your husband is already this concerned about how "cool" and "tough" his son appears to other kids at this young age, what disagreements will the two of you be having in a few years' time? Will your husband get him a motorized scooter and insist a helmet's not cool for that either, or for a big-boy bike? Will coolness override basic safety in other discussions on lifestyle and choices as your son grows up? And is your husband really showing you respect when he dismisses your legitimate concerns in the name of appearances and the opinions of -- who? Your son's fellow four-year-olds at the playground?
If he's really adamant about this I'd find a friendly cop to talk to him about the local law and maybe some real-life examples of kids being hurt. Or find other dads who encourage helmet-wearing to talk with him.
And it's an adult example, but my coworker's life was saved by his bike helmet. He fell, not far, but his head hit a metal pole--hard. The doctor said he probably would have died if not for the helmet.