I live in Norway. Here the snow have just began and is getting heavier day by day. Therefore we need a shoe which protect our feet in this cold weather when we are outside. There are a leather shoe which I found, but it has pig leather. Other leather are really expansive like cow leather here. Our only option is pig leather or none. Is it permissible to buy shoes that have pig leather on it?

Yes, you can buy the pig leather, but your intention should be that you are giving the money to the merchant to allow you to take the product, since selling and buying pig products is not allowed. However, if your feet got wet, or if it touched your clothes with wetness, then you need to wash them.