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!
Yes, bringing the crawl space into the conditioned space is generally recommended as a way to prevent crawlspace moisture problems (I assume this is what you mean by encapsulate).
This means:
- sealing vents to the exterior
- sealing the dirt floor with polyethylene sheeting (at least 6 mil), or concrete
- creating vents between the living space and the crawlspace (ideally supply air to/from the space with HVAC ductwork), and
- insulating the interior side of the crawlspace walls on (not necessary in climate zone 1 or 2; and preferably with board foam or spray foam because fiberglass doesn't do well with moisture).
- probably a good idea to remove existing floor insulation
This will prevent humid outside air from coming into the crawlspace and condensing on cold surfaces, and prevent/reduce moisture from coming up through the dirt floor or walls. Your AC will also deliver cold air more effectively. Good site drainage is also key.
There are many good references on how to do this properly:
http://www.housingzone.com/crawlspaces-vent-or-not-vent
https://buildingscience.com/documents/bareports/ba-0401-conditioned-crawlspace-construction-performance-and-codes
Best Answer
Most of the jurisdictions in the U.S. use a version of the International Residential Code published by the International Code Council (ICC). You can call your local Building Code office to confirm the minimum requirement and if you need to purchase a Permit.
The Code requires crawl spaces through the exterior perimeter wall shall be 16” x 24”. (See ICC R408.3) The code doesn’t indicate which way the 16” is required, vertical or horizontal. If the opening extends below grade, then you’ll need to provide an opening like a window well too.
Most exterior walls are load bearing, so you’ll need to reinforce the floor with a header for the part that rests on the opening. However, if you choose a side of your house that has floor joists running parallel to the opening rather than perpendicular, you may be able to skip the header.
I’d contact a local carpenter or general contractor to do the work. (Make sure they are licensed in your jurisdictions.) If you don’t know of a good contractor, I’d contact a local architect and ask for a recommendation.