The more I thought about this it reminds me of a mild case of Trench Foot. This is what soldiers suffered in WWI caused by cold, wet and insanitary conditions while standing in flooded trenches for long periods of time. Mostly you need to keep your feet dry and clean, at your next tourney perhaps having a pair or two of clean dry socks to change into after the first round and maybe even a pair of spare shoes/boots if yours are wet. I wear Seal Skinz in the winter over my regular socks. They are completely waterproof but let your feet breathe at the same time. You can get those at REI in Ann Arbor for about $30. Here is a link that has some tips for preventing the symptoms of Trench or (Immersion) Foot from happening in the future. http://www.bt.cdc.gov/disasters/trenchfoot.asp
I think Mike is correct that what you are experienceing sounds like Trench foot. He is also correct that the best preventitive is keeping your feet clean and dry. Changeing socks helps a lot. I also have a couple of pair of those thin socks that wick moisture away from your feet. I can't remember the name but I got them at Sports Authority.
What I find most helpful to prevent the swelling is wool socks. Companies like smartwool and others make socks that are a bit thicker for Winter gold. That said, following injury, I use Weleda Arnica massage oil. You can get it at most health places ie Whole Foods, Coop's, in A2 there is Arbor Farms, Plum Market. Anyway, Arnica is a homeopathic remedy. It helps with sprains and strains, muscle pains etc. Costs about 15-17 a bottle and can last a long time. Also, soaking your feet in epsom salt will help with the swelling. For us older dude's soaking in a bath with about 10-12 drops of the Arnica oil will take the muscle aches away in about five minutes. I know it's not a pretty picture but it works well
I suffer from the sore feet after a couple of rounds... during a break between rounds I like to put on a different pair of shoes for a bit... In the nice weather I throw on my Crocs ( I know they are the ugliest shoe ever made, but they are nice and soft ) Fresh socks, and dry feet make that 2nd round so much better. Lots of water and munchies seem to help reduce the aches and pains... lots of advil helps also!
as people have said, keeping feet dry or changing socks and drying them out will help, but also...
in the wintertime i find myself only realizing something is wrong or hurt after i warm up. be careful not to push to the point of injury just because your feet are too cold to feel them hurting. try to warm them up in the car or by a fire between rounds and consider the toe warmers (i even know a guy with battery powered socks) to keep your feet to where you can feel them. if there is a problem beginning, and you are unaware, its bound to just make it worse during the round. make sure your shoes are big enough to accommodate the thick socks and or sealskins, because cramming wet feet in shoes too small will also perpetuate your problems.
Your boots might be the problem. Your foot moving around in a hard leather shell especially with wet sock can wreak havoc on your dogs. I think you mentioned snow, maybe you could splurge on some gore-tex trail shoes and some gaitors to keep the elements out. Does this happen in more favorable weather?
For the best remedy, come down to Charleston, SC for some R&R!
I think Mike might have hit it on the dot. My feet were soaking wet and cold for a long period of time. I also did some research on it and found that could be the problem. I will definitely carry a couple more pairs of socks with me.