Is there a top breathable enough and water repellent enough to work in those conditions?
I think it depends on the specifics of your snow. I’ve never had snow penetrate my Ferrosi. Heavy rain does. For sure the Ferrosi is well more robust than a Dooy — to the point that they are nearly two distinct classes of garment.
Another thing to consider is warmth under your shell, for two reasons:
1) Your main complaint was cold. -5C sounds like the edge of the performance envelope for Lifa+Dooy under good conditions, and clearly it was insufficient when also wet.
2) Warmer insulation means that your jacket can be cooler, so maybe wouldn’t melt snow as quickly.
I would think that another layer under the shell, or perhaps your Houdini over the Dooy in wet snow, might be worth a try.
I mean, the Houdini might be sweaty, but at least you wouldn’t be so cold.
Even a fishing shirt between Lifa and Dooy might be enough to keep you both warmer and dryer.