Firstly, do not self-medicate. And do not take online medical advice : go see a doctor.

The reason you have foot pain is that your blood is thicker : it has a harder time flowing further away from your heart. This has 3 consequences, not just one.

1) is feet, or other extremeties, not getting enough oxygen. This will result in weird tickling, then numbness, then necrosis, which will hurt.

2) is nerves deteriorating or dying in your extremeties due to repeated instances of 1. This can lead to pain upon the slightest stimulation. Someone touches your feet and you feel like a needle has been stuck entirely through your foot.

3) is too much sugar in your blood. This is why it's thicker. This will result in a big boost to whatever bacterial infections you already have in your feet (we all have a few).

If you must take online advice then please:

First, a number of things have now become really stupid. First on the list: you need loose fitting shoes now. Note: not sandals. Sealing your feet in "flexible" sport/running shoes can worsen your condition rapidly, especially if you lace em tight as well. Likewise walking around barefoot is stupid, especially outside. You need comfortable and fresh socks at all times, and you should not walk around without having your feet covered, given what can happen if you hurt your feet.

Letting your feet freeze, even just to a point that would be fine for normal people, has just become stupid. If it happens anyway, fix with water. Start with ever so slightly warm water and slowly raise the temperature. What works best is having warm water flow over your feet. The point of this is to warm the blood going through it, so despite how it feels the first moment that this actually has an effect is 2 minutes after you've started doing it. You want to do this for 4 minutes absolute minimum, but 10 minutes is certainly better.

Second, when you feel this happening : change your posture. The easy way to provide relief is to lower pressure, and you do that by making sure the vertical distance inside your body is minimized, and nothing is pushing on anything else (e.g. crossed legs, sitting on your feet or knees, ...). If possible, lie down, if not, at least sit down. Change position regularly and move.

Aspirin can help, but go easy on it. You might consider having the lowest possible dosage you can find, and just taking it constantly. Needless to say, you should discuss with a doctor first. Be careful about mixing alcohol and medication, even in small quantities.

It may also be good to have a "training regimen": stretch your feet every day at least. Move every toe forward and backward a few times using your hands and bend the foot every way it'll go a few times.

Thirdly, if you don't keep your feet impeccably clean, I guarantee you you will regret it. Warm (not hot, warm) water, twice a day, at least. If your skin dries out skip the soap one out of the two times, or find a better soap.

Fourthly, any slight wound to your feet can infect like you wouldn't believe and result in amputation (or death). If your cat playfully and slightly breaks the skin on your feet, and it doesn't even hurt, you still have a doctor clean it and prescribe antibiotics for a day or two. Serious wounds need to soaked in alcohol (medical alcohol, vodka works but is not as good, so only for emergencies). You go back for checkups.