Converting roman concrete formula for cold weather environment

I never use reddit, however a clients request has me stumped. They are planning a project to build a home using middle-eastern / roman building practices and techniques in USA climate zone 3-4. The plans for this are relatively sound albeit a bit strange for the region they have picked (namely a large courtyard) but have made significant efforts to accommodate for this. Their budget is essentially unlimited. One particular request that they have been an immovable object on is the composition or formula for the concrete used to lay the foundation, first story walls and facade. They are insistent that it is not just similar, but the exact same composition found in ancient roman architecture like the pantheon and whatnot (volcanic ash, quicklime, aggregate, pumice, etc.) I'm worried that it won't be as structurally sound as other concrete mixes, especially given a freeze-thaw cycle in northern climates. As ideas to perhaps modify or add a material to increase structural integrity?