A very common mistake is to insulate a floor of a basement/crawlspace and not the walls, when in reality the cold comes in from the sides. A lot of people make the assumption that insulated floors make warm floors but that is just not so. The laws of thermo dynamics come into play here, and no insulation ever invented is going to stop the laws of stacking. All insulation in a basement or crawlspace does is keep cold floors cold, and give rodents a nice place to live while increasing the cost of building the home. Worst yet, after a few years of moisture condensation, removing the nasty insulation ladent with rodent feces and
urine will not be a fun job, or expensive if it is hired out. There are a few exceptions to this, but mostly in split level homes.
The great news is, you may be able to get out of this pretty cheaply.
Drop down into the crawlspace and take a look at the rim joist. If this does not have insulation, IT NEEDS IT! Thankfully, that may be all you need.
A lot of people think hot air rises, but this is actually incorrect, cold air is more dense then hot air, so it sinks. This is a huge difference, especially in your home.
A house is heated via a few different ways, but mostly by convenction. Think of this as a rolling swirl. Cold ALWAYS goes to warm, so as the air around your ceiling is warmed, it is stopped from rising by your attic insulation, BUT now cold wants to go to warm so a vaccum is present. Without insulation in your rim joists, it is sucking that cold air from outside, under your walls and then up through the floor and into your home. This then starts stacking up, cusing that swirling effect. The more air iniltration in your walls and crawlspace, the faster this swirl happens. Just keep in mind, this vaccum is present 24/7 during the heating system so any way cold air can get in (not warm air getting out) can make your home harder to heat.
In your case, your home is "stacking" cold air down at the floor level, and in your crawlspace freezing your pipes when it is really cold.
You need to keep the cold air from coming in, but that is done at the walls in the crawlspace, and via two ways. Insulation (and your rim joists may just be
enough), and air infiltration. Think plastic, caulking, really anything to stop air from coming in. This includes in the living space around any penetration that goes outside; doors, windows, pipes, around outlets, etc.
Sadly your floor is covered in concrete because a dirt floor lets in a lot more "heat". I put heat in quotes because the ground here in Maine anyway, always stays 57 degrees so it really is helping heating a house compared to the fridgid cold outside. As I type this, it is 20 degrees outside, but my dirt floor, fieldstone basement is 41 degrees because of what I say is happening. But you have what you have and that is fine, no need to rip out the concrete.
So I would insulate your rim joists, which
should be really inexpensive since you are not doing entire walls. If that is not enough, you might consider "banking the house" which is what we call it here in Maine. I did this yesterday, putting
hay all around the edge of my house to stop the wind and cold (but I have a fieldstone foundation too). If that is not to your like for asthethic reasons, you can insulate your walls by furring out with strapping and insulation.