Need Ice Bath Tips

So had my first ice bath on Saturday due to running 2 longer runs at the weekend instead of a shorter run and a longer run (still not very good at the running so 13miles on Saturday, followed by the Kilomathon on the Sunday which is 13.1km), decided to try an ice bath after the Saturday long run to help with the recovery for the Sunday run.
Ran the cold water and got in making sure that the water covered the tops of my legs, then added the ice.
I had filled a bin bag with ice from the restaurant that I work at and it was enough to put a layer of ice across the top of the bath.
kept my running tights on and my running tee and warmer base layer on as well, however my feet and toes got REALLY painful, should I have kept socks on, or just suck it up??
Managed 12min before getting out (because of the pain in my feet), whilst it wasn't pleasant I felt ok for running on the Sunday and was pleased with my time and felt ok yesterday, I would use them again at the weekends for after my longer runs (fortunately my longer run this weekend is down to 10miles so probably won't need it this weekend but goes back up to 15miles the following weekend).

Any tips for my feet appreciated:)

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