A cross maybe good. I raise Single Comb White and Rose Comb Dark Brown Leghorns. In the past few months I have lost 3 of the White Leghorns to predators. The 3 Houdini's. They could find a way out of any coop and pen I put them in and would get out any chance they could. All three eventually disappeared. I found some feathers behind the coops but the other 2 just vanished. The rest stay in their pens until I let them out.Do you want a cross, even if there's one breed that fulfills all requirements? I have found that Leghorns are range-wary, intelligent, capable of enough flight to get away from dogs, incredible layers, and cold hardy. Even the whites, which are single combed. Yes, they get frostbite, but that's only one measure of hardiness, and there are rose combed varieties that still lay like gangbusters, according to what I've heard.
My hatchery line Leghorns were out and about on weeks when the highest temperature didn't even scrape 0*F and the lows were much colder. They have ample and stiff feathering that still possesses plenty of down. I have found that cold hardiness seems to be rather connected to temperament—the 'calm' breeds sit on the roost and shiver themselves to death, and the feisty breeds get off the roost and eat and drink and stay alive.
If you want to do a cross, I'd put American Gamefowl into the Leghorn and see what it does. If you want DP, I'd add Chantecler. They're almost as hardy as the Leghorns. A bit sillier about snow, but very good winter layers. Most of my birds shut down in winter, even the first year pullets, and only the Chanteclers and Leghorns lay through.
I wouldn't do EE's for rate of lay or flight. I found them average at best in both respects.