Good question, let me break it down into three parts that address your major concerns:1. We have a contractor who says we should use a two-inch thick closed-cell spray foam in all the stud cavities. My concern here is that essentially this creates the vapor barrier on the OUTSIDE wall, and the remaining four inches of the stud bays are open to interior moisture. Could that allow warm moist air to condense on the studs that are colder (due to cold conduction from the outside), leading to mold and wood rot?We went to the experts at Icynene for this one. With two inches of closed cell spray foam, the vapor permeance of the spray insulation will be very low and may serve as a vapor retarder. In climates such as yours (Oswego shows 6792 Heating Degree Days or HDD), which experiences less than 7200 HDD, we prefer to see the system breathe (i.e. no vapor retarder), which will facilitate drying to the interior in the summer and to the exterior in the winter. Wood studs are a thermal bridge, but they aren't as bad as some materials such as metal. Wood, for example, has an R-Value (which measures resistance to conductive heat flow) of about R-1/inch, so your 2 x 4's have an R-value of about R-3.5, which reduces a fair bit of the conductive flow (80+%). Wood would not be a significant factor in thermal bridging when a thicker layer of Icynene® (a flexible open celled spray foam insulation) is used to insulate the cavity. The key to energy efficiency and moisture management is creating an air seal around the building envelope. Materials such as rigid foam (closed cell) materials can be subject to the shifting structure during freeze/thaw cycles, which may lead to delamination (splitting or separation) from the substrate or cracking that can compromise the air seal and energy efficiency and lead to potential moisture problems. Icynene® (an open celled spray foam insulation that is not a vapor barrier) - would be an excellent spray foam insulation choice for this type of climate.2. It is my understanding that wood needs to breathe, especially if it gets wet.If we do spray foam, then we will end up applying spray foam insulation directly to the back of the house's sheathing (and in some cases, the original Dutch lap siding is nailed directly to the studs, there is NO sheathing). If any water at all gets behind the siding (as in between the siding and the spray foam), wouldn't it get stuck there and be unable to dry out because the spray foam prevents air circulation?We don't have any known major water problems, but this is a huge, 3-story 130 year old house and some water in some amounts, especially during the ice melts in the spring, may enter walls in places we may never know about. Maybe over the last 130 years water penetration has not been a problem because the exterior walls breathe, but with spray foam might we introduce a problem in this manner?As mentioned in our response to your other question, we recommend that the wall system breathes in your climate (i.e. is vapor open). In areas where there is exterior sheathing attached to the studs, a product like Icynene® spray foam insulation may be applied directly to the sheathing. In areas where the lap siding is attached to the studs, you must maintain an air space to handle the liquid moisture, which WILL enter through the laps. This requires installation of an alternate substrate such as landscape cloth, Tyvek, or cardboard baffles etc. to maintain that air space between the insulation and the lap siding.3. A major concern I have is investing 15-20K in scraping and brand new paint, only to have it peeling off the siding in two years because moisture is trapped in the siding and outgases from beneath the paint because it has no where else to go - on account of having airtight spray foam insulation.As stated above, (in response to your earlier question) in areas where the lap siding is attached to the studs an air space must be maintained for moisture control. If that space is eliminated the paint will peel in these areas due to excessive moisture buildup and lack of ventilation to dry out wet areas.