First stop is obviously docs. Sounds similar to an injury I had. Non-freezing cold injury.
Get yourself a foot spa and begin using daily as often as you can. That'll promote circulation for starters.
The pins and needles will probably replace itself with a constant numb feeling. This is due to the capillaries in your feet having shrunk and being unable to get the necessary blood flow around your feet.
Get some warm winter socks & avoid exposing them to any cold. Get some warm footwear, that'll keep your feet insulated from the ground.
My numbness lasted for 7 months although that is a more extreme length of time.
The docs can have you forwarded to a specialist who will undertake an assessment of the extent of the damage by taking a thermal image of your feet before & after exposure to cold water, as well as doing a hot/cold feel test on you, similar to a hearing test.
Unfortunately, it's a bit permanent in the more extreme circumstances but by rapidly acting, you can reduce the damage.
***My experience comes from actually having had an injury where the symptoms matched those described, I'm not a doctor so seek expert advice.***