Where could the water leaching from the base of the drywall be coming from?
To a certain extent, moisture is unavoidable during construction. However, this is why you don't build in winter, especially in your climate, because the surface temperatures of many smooth materials (your windows, tile, plaster) are going to fall below the dew point, especially if the heating system hasn't been installed yet. When that happens, any moist air nearby is going to condense on them and turn into liquid water.

Since you can't change the season, and you can't remove the surfaces that are receiving condensation, if you want to cut your losses, hurry up and install the heating system right now, or else insist that construction take place only in the presence of construction-grade space heaters and dehumidifiers to keep moisture down and the interior heated to above the dew point.

Finally, I hope you don't have poly sheeting under the drywall. If you do, it would be worth it to eat the cost of removing the drywall and the poly sheeting. This stuff is incorrect to install, as it is a smooth vertical surface that will receive a lot of condensation when it falls below the dew point temperature. A lot of moisture is present in adjacent materials during construction, and if it's cold out... do the math. Your walls are going to weep like crazy and present an ongoing problem.

More worryingly, it sounds like your general contractor doesn't really know what he's doing. You should not be building a house during a cold upstate New York winter, and your drywall should not weep during construction due to un-dealt-with moisture loads. Additionally, 1" of foam outside the sheathing is far too little for your climate, and kraft-faced fiberglass batts are the worst, lowest-grade insulation out there; they perform very poorly.