We have those gulleys (I think that's what you call them) that have a metal grid cover over one half, and a pointed up drainpipe going into the other. Over the years, some of the pointing has broken, so some of them are open on the drainpipe half. I expect the frost does it. I've always meant to do something with them, but it was never a priority until our three year old boy started throwing handfuls of chippings down them, and I'm fed up of unblocking the things. Plus, the neighbour fished a dead hedgehog out of one of his.
Anyway, I was wondering what you'd cover the hole up with before starting to point it. My father-in-law used to nibble a piece of slate into the right shape with a pair of pliers, but I'm not going to be able to reproduce that :) Or is there a completely different way of tackling the problem these days? I don't fancy those big plastic covers.