My DD ice skates and roller skates... Until this year (now homeschooling), it was even part of her school's phy ed program. It never occurred to me not to let her participate. (They also set up an obstacle course every fall, and visit the ropes course at the high school)
We also ice skate as a family a few times per year, and roller skate with another family 3-4 times per year, at least. Plus bday parties or friend invites.
That said, my DD is a naturally cautious kid. If kids are being reckless, she will sit out on her own volition.
As for snow sports, she does refuse to try those - to afraid to get hurt in general. Though I do let my (much less cautious) gymnast DS take ski and snowboard lessons, and being MAG, it's during the season.
I totally get some families not wanting to risk it, but for us, these are just "normal" activities, and not a whole lot different than riding bikes, swimming, using diving boards, etc. There's always some risk.
To OP, do what is comfortable for you, but for me, I'd consider my DD's wishes.