I agree with the others.
I started last year with a rain blanket for my horses (after 3 years without) and I was also told that it would flatten their fur. But I started late when they had already a nice winter coat (it was a dry autumn here), and I'm going to use the rain blankets this winter too! They were actually quite happy about the blankets, one had never been blanketed in her life (and she is the one that is often kept "out in the cold" because the other one doesn't want her in the shelter) but she immediately found out that the rain blanket was quite nice and kept her dry.
I also prefer to put on a rain coat over my woollen sweater when I'm out in the rain