Freezebranding, yes, the hair grows back in white...generally. However, on a horse with white hair, the iron is supposed to be held on the body longer to completely kill the hair follicle so that no hair would grow back in at all. Essentially, that would give you a brand that was the color of the skin underneath. Black in appearance on a gray horse and pink in appearance on a white horse. Really no different in that aspect than hot branding, just a whole lot less painful.
I've never been able to find a picture of a paint horse that had been branded inside one of its paint markings but I've seen some of them in real life. The brand on those horses are generally not any harder to see than a hot brand on a dark colored horse.
For example. Here is a really bad example of a freezebrand on a gray horse. They didn't hold the brand on quite long enough to completely kill all the follicles so there is still quite a bit of white hair growing in. You can't see the brand at all in the winter
but this is what it looks like in summer
It's really no different than this. This horse was hot branded on his hip. Can you see the brand or make out what it is? Me neither without walking right up to him and looking close at the location where I know
the brand is
We'd had him for several weeks before I even noticed the brand, it was so faint