My goose has an infected foot

[Puddlesgoose]

I agree, it appears she is losing circulation to that foot most likely from the injury than anything else, as waterfowl tend to fair cold weather extremely well. You could either let nature take its course and see how the leg fares, or euthanize her. The problem that's often apparent with these birds is they develop secondary conditions.

For example, judging from the picture it appears your goose is developing a sore on legs hock because she's applying more pressure to that area. Left untreated, that area will become infected and she will be left with another infected part of leg. You'll also likely start to wet feather develop, arthritis, sticky eye, and overall poor condition if they're not cared for with extreme attentive care.

A lot of birds just go down-hill after things like this, but if you want to give her a shot, for the leg, I may soak that leg in Epsom salts often, and start applying an antibacterial ointment to the area once a day to help ward/fight infection. Ensuring she is getting in deep water daily to relieve the weight off her legs, and making sure when she's not in water, she's on soft padded grounds to prevent sores would be a good idea. Keeping her on a diet formulated for waterfowl like Mazuri, and adding B vitamins, greens, and omega-3s may help prevent, and treat ongoing leg issues.

Ok, thank you for the advice