I can't tell for sure based on the picture, but it looks to me like you have the roof deck on the left, and a knee wall on the right that separates an already finished portion of the attic from the area pictured, like this:
and you are considering utilizing one of the areas labeled
Attic 1 as the closet.
If that is correct, you may already have a slight problem: with this type of attic, and in areas where significant snow can accumulate and cold winters are the norm (like Connecticut), it is usually better to have what is referred to as a
cold roof. This means placing insulation on the walls that are green in the diagram, and leaving the roof deck un-insulated. Combined with good ventilation, this allows the attic to more closely match the outside temperature. In turn, a cooler attic reduces the amount of melt that occurs after a snowfall, which prevents ice dams from forming when all that melt water reaches the exposed eves and refreezes.
The alternative, a
hot roof (which it looks like you might already have) greatly increases the likelyhood of quick snow melt and ice dams. There is just no way you can put enough batted insulation in there to keep the heat from warming the roof. I suppose it would be possible to combine the two (insulating the green walls and the roof), but ultimately, any increase in temperature in that attic space is going to warm the roof deck. Similarly, if you block off the air curculation from the attic vents, the result will be a warmer roof.
Would it be possible to remove the roof deck insulation completely, and instead insulate the wall on the right in your photo? You can still build a closet in there, but it might be best if you left it unheated and well ventilated (as much as your wife may not like a cold closet, it still beats a leaking and damaged roof). If you totally finish that space and increase the heat loss through the roof, you might end up growing some record-seting icicles once winter sets in.
Source: I live in Minneapolis, and I have this type of attic setup with the hot roof (not my doing). My eves are lined with the most fantastic icicles in the neighborhood.