It is natural in some species.
If you have a photo it would help in telling if there's something wrong.

Thank you. I have updated my question with some photos.
I haven't had the cactus very long and I'm still learning how to care for it.

It's a lovely plant and there's nothing wrong with it - woolly hairs appear with new growth on many cacti. That's how it's supposed to be.

Thank you!

That's a beautiful cactus. There's nothing wrong with it. That stuff keeps the bugs away. That's just how it grows.

the fine hairs help maintain a moist micro-climate for the growing tip. Many cacti have 'fluffy' hairs to reduce transpiration/water loss. A brilliant adaptation to living in a hot / dry climate.