I need to store a no yeast dough (water, flour, butter, salt) for verenyky for about 40 hours.
What would be the best place: fridge or freezer?
I suppose we are talking about pâte brisée / salty pie crust or similar dough?
As 40 hours is scant 2 days and you are not using any ingredients that will spoil quickly, a fridge should suffice. Advantage: use right away w.o. thawing. Also avoids condensation from thawing, but propper wrapping should take care of that problem anyway.
My calculation: If you freeze the dough it'll need a couple of hours in the fridge to thaw, so assuming 2-4 h until frozen, 6-8 h to thaw (depending on shape): What difference makes 30 h at -18°C instead of 4°C?
I'm speaking from 30+ years of experience (we make a LOT of cookies here in SW Germany around Christmas). Neither my Mom nor I ever had mold problems after two days in the fridge.
One drawback though: If you prepare the dough and don't get around to baking it, the feezer would have been the better choice.
EDIT after clarification:
I guess we're talking something akin to pasta dough here? IMHO the same principles apply. I'd be a bit wary if you use eggs. Use fresh eggs or pasteurized, if you can get them.
Dough grows moldy in the fridge after several days. While it might keep 40 hours, it's more secure in the freezer.
Depending on what you want to make with it, it might be better to work it from cold or from warm. If it is better from cold (e.g. pie crust, pierogi should behave similarly), freezer is perfect. If it is better from warm, you'll have to plan for sufficient time to unfreeze and let it warm up. In this case, the fridge might be better despite some mold risk.