I put my toes in some water with ice cubes after most of my runs. I have morton's toes, I think it's called (second toe is longer) and it's always tender. I do it to get the blood away from my toes to help prevent black toenails.
I'm not sure if you're supposed to do your whole foot or not, but I find it helpful for my toes.
If my run is longer than an hour I put a sweatshirt on and run cold water in the tub until it covers my thighs. Then in goes a 5# bag of ice. Soak for about 10 minutes (or as long as I can handle it) and then take a normal shower.
No soreness the next day even after a 2+ hour run.
Do a search on "ice bath" on this forum and you'll see that is a very common thing to do to help repair what you do to your legs on a longish run.
The only time I've iced my feet after runs was after really long runs during marathon training. I'd do an ice bath after those and be a lot less sore the next day. I didn't bother for any of the weekday runs.