Mostly landowners will frown upon you if you have a camp fire, but if you do it right, they have nothing much to complain about. Never just start a fire on the ground, this leaves a horrible mess afterward. Use a spade to lift the turf of the area where you want to have a fire... Put the turf to one side upside down. If you have peaty soil, replace the turf and look elsewhere, if you have sandy soil go ahead and make a contained fire in the area where you lifted the turf. Firewood can be found in abundance in any woodland or forest on the forest floor. Never ever cut live wood or tear the branches off a living tree as this is bad conservation and unnecessary. When you're done, make sure the fire is out, using plenty of water, scatter the ashes and unburned pieces in the river, then replace the turfs and gently stamp them down. - the idea is to leave the landscape as you found it. If you're on snow, you're going to have to do some serious digging before you even reach the ground (Which will be frozen), so think about if you really need that campfire afterall.
Sometimes, firewood will not be obviously available, so you'll need to take advantage of local geology and burn peat , seaweed, oilstone, bogwood, or whatever is available. If you're having a campfire, you can burn any litter you have, But not tin cans, (Although they will burn if hot enough, you're camp fire ain't going to do it)