Found this question on the FAQ section of Nokian Tires (
http://www.nokiantyres.com/faq
(Although the question was asked for studded tires, I am pretty sure the answer is valid for all directional tires)
I mounted one of my studded tyres against the rolling direction and drove it like that through the winter. Did it damage the tyre?
The tyre does not get damaged when it rolls against the specified rolling direction. However, it is recommended that you do not change the rolling direction of a studded tyre during its useful life as this may affect the grip of the studs on the tyre. To achieve the best possible cleaning and slush properties, the tyres should be mounted in their correct rolling direction.