No. (unless I'm in a combat zone with bullets and shrapnel
I'll never discourage anyone from wearing a helmet. I even require my little grandchildren to wear them as they learn to ride, but I won't always require it of them.
On the "safety" side:
1. Every person I've known who has died from coming off a horse was wearing a helmet (but the neck still breaks anyway). The worst injuring in my family was a cousin who went into the trees when a run-a-way stumbled and flipped (she broke an arm, broke her shoulder, cracked ribs and had a hip injury, but even without a helmet her head was fine).
2. The head suffers the smallest % of injuries from coming off a horse (they usually put the head and neck together just to get the numbers up and even then it's the smallest %) Most injuries are to the upper extremities (hand, arms, shoulder). Next are the lower extremities (hip thru feet) and then the torso. The head comes in a distant 4th. It is true that you are more likely to die from a head injury than upper or lower extremities, but then that's true if you're walking you dog and a car hits you....do you wear a helmet to walk the dog?
It's all about what are the odds.
On the practical side:
I don't ride indoors or rings unless there's the rare specific need to so I ride outdoors in the weather (rain or shine if it's not too hot) and for days when time permits. Helmets result in either a massive case of sunburn or spending time every hour reapplying sunblock to all of my head and neck. If it rains the helmet does nothing except the allow the rain to run across every inch of my head and across eyes (thus impeding my vision). I like keeping sun off and the rain channeled away from my face.
I worry more about my back (which has a much higher chance of being injured) and my neck which the most fragile area and probably accounts for more of deaths (certainly that I'm familiar with) and crippling injuries than the head.