Your daughter is absolutely adorable! She's lucky she's growing up with horsey parents - I had to nag my parents into everything horse related.
Anyways, to answer your question: yes, I do wear a helmet every single time I ride. You just never know what's going to happen when you get on any horse. My favourite example: my old horse, even though I only owned him for two years, I had been riding him at his old home (I bought him from a lesson barn where I had been part boarding him and moved him to the barn I work at now) and he was one of the laziest horses ever - took a long time to get him working nicely off of your leg. Well, one day we were just trotting nicely down the long side of the arena and it all happened so fast I barely remember it - at first I thought he was cantering, and then I heard my coach yelling at me to SIT DOWN and we went around the corner, the stirrup broke (I was wearing peacocks) and I went flying into the wall. My head hit the wall before my body hit the ground. I looked at my helmet afterwards and it was concave where it had hit the wall - and this wasn't a cheap one time use plastic helmet. This was a nice expensive IRH helmet! Well... we will never know what spooked him that day. I got back on after and schooled him as normal and he was totally fine - rode fine for me. But I still had a concussion even with that helment on, that's how hard he threw me into that wall. And I will never forget that day for as long as I live and how glad I was that I was wearing that helmet.
Now, obviously, if you're riding a horse out in the open field roping cows then there's little to no chance you're going to be thrown into a wall. But it's way better to be safe than sorry. I'd rather wear a helmet, look a little dorky, and still have normal brain function than have looked cool and be lying in a hospital bed as a vegetable.
But that's just my opinion on it... I'm totally aware that at speed events you will get laughed out of the stadium (when I did barrels I was 14 so I had to wear a helmet anyways) so if you do that then I get that. But to me, not wearing your helmet is like not wearing your seatbelt in the car. It's there, it's extra protection, so why wouldn't you use it? My 2 cents.