I thought there was something akin to a gutter, but not with a trough for
water, that would disperse water as it came down the roof to the edge.
Obviously it would not catch any rain water but simply disperse it out over
the roof edge. Does something like this exist?

I was thinking that in order to eliminate gutters clogged with ice in winter
months if I could just allow the water from melting snow to just disperse
out over the edge of the roof to the ground below.

If nothing like this exists or if it just wouldn't work then......never mind
(or...fugedaboutit).

Thanks,
Walter