I'd only ice it if it hurts.

Are you really tall? I suspect from your photos that you are. If so it is a LONG way to that pinkey!

Arginine is in some diabetic foot creams to increase circulation.

The Magnesium lotions do the same thing. So I'd start there. Magnesium also blocks the NMDA pain receptors, so it is more useful than arginine.

You could combine the heat treatments followed by ice... see how that goes. Don't over use cold though, as that constricts blood flow.

Think about how your hands feel in the snow without gloves. Then you come in and warm them up.... and they get red and tingle and burn! Same thing with that pinkey. If it hurts at bedtime do the cold treatment then. You will not be standing up and the blood flow with return to normal quickly, when you are sleeping.

Injuries can take a while to heal. Give it time. Don't worry about neuropathy at this point. You just have a trauma toe.
I'd take some vit C daily.... 500mg for about 2 months. Also so other antioxidants, if you want. Some people develop RSD from injuries or surgery or trauma to the ankles/feet and wrists. Vit C seems to block this potential. Since you are taking a while to heal you will want to prevent RSD.

RSD patients however do hate cold treatments, and prefer heat, so you are still the reverse of that. RSD may become permanent, but studies in Europe show Vit C prevent that for many patients.

Keep your foot elevated when you can, at home, etc. I had a surgery on my foot when I was 12, on the instep and it took over a year to heal. Foot injuries take time.