It is a good idea to seal any apertures between the crawlspace and the main house. If you have to rely on caulk and spray foam you're probably in a situation where the house has some weird structural problems - that is, you should not have giant gaps between the crawlspace and the floor above in any normal construction regimen.
It is not a good idea to seal off the crawlspace, ventilation is not only a good idea but it's required by code in locations where crawlspaces are an accepted norm (note that in places where winters are exceptionally cold the norm is finished and unfinished basements, not crawlspaces). The fact that you have had mold in the crawlspace is actually an indication that you might need MORE ventilation not less.
A proper insulation/vapor barrier installation at the level of the floor joists should solve any draft problems. Also, looking at your photos I would recommend that you insulate your ductwork/boots/wyes per local code.
So to reiterate, please do insulate and install a vapor barrier! Do not seal off the ventilation for the crawlspace - indeed look into your local code to see if you have enough ventilation.
As a side note - any issues of moisture (and therefore mold) in the crawlspace need to be addressed. Possible sources of moisture include but are not limited to: leaky plumbing supply or waste lines, inadequate drainage system at the perimeter of the house (undersized gutters/downspouts, poor grading, no storm drain, etc.), and a possible high water table.
Good luck staying warm this winter!
I am also in the Northeast and have had to tackle this type of situation a few times. There are several ways to attack it.
In your case, the best solution, but unfortunately the most expensive would be to use an open cell foam kit to fill the joist bays. They are fairly easy to use and give you about an R-4 rating per inch. They are a two tank kit with a hose and wand.
Here is an example product: Touch N Seal 1000 Kit Open Cell Spray Foam Insulation
These type of kits start around $400, depending on the square footage and depth required.
A cheaper method would be to use 24 inch R-19 unfaced blanket insulation cut to your custom widths. You can use wire springs to hold it in place and keep it from falling. I would then cover the entire area with 4 to 6 mil plastic, stapled to all the joists. Tape the joints, if any. Moisture should not be a major problem since you have already done what sounds like a good job sealing the dirt floor. In the summer months, some ventilation in the crawl space will also help avoid excess moisture.
Rigid foam glued to the foundation walls would also help if the area is fairly air tight. If there is free air flow, insulating the brick walls would be a waste of time and money.
Best Answer
Should work fine-ish. Use more UN-Faced insulation to avoid moisture problems.
It's only fine-ish (rather than fine) because the pipe is more than halfway through the total insulation, leaving it somewhat subject to freezing if it gets cold in the crawlspace.