I must confess to never having worn a cloak on a gurt big hill in a gale force wind; I must try it some time. :-)

It really sounds like you (a) need a smaller hood and (b) no slithery fabric. Try wool, cotton and or linen. Get a nice wool outdoor cloak, much warmer and more practical in unclement weather. I think I paid fifty quid for mine, the pure wool ones are a bit, but not much, more.