No, absolutely not - this grass is only frost hardy, so let it die down naturally, leave the dead stuff on and pile leaves or something over the top to help protect it during winter. Remove all the dead growth in late February, unless its still freezing, when you can wait till March.

As Bamboo said be sure to cover it over. I did not cut my newly planted one back but neglected to cover it and it didn't survive the winter.

I don't cut my blood grass down until the spring, but it doesn't get any other protection. It was planted nearly 20 years ago.

I'm not surprised in your garden, Andrewr - you've managed to create a micro climate...