I am on the same hunt as you. The issue I have run into for the 3 different pairs I have tried is the height of the boots. They are too tall, I can't get them to go up as high as they should so they are all the way on. Maybe our mini is extra short?
However, I found one pair that work okay for now that I will link below. They are not particularly warm, but we use them to keep his feet from becoming wet in the snow. We don't get heavy snow where we are, so I am not sure how well they would hold up if the snow went high above the sole over the top of the foot.