Do not approach the shack, nor the soldiers here, up front, but through the snowdrifts from, the back side. This will allow you to eliminate opponents without taking the risk of being spotted. Get rid of the one on the left, in the first place. This will attract the attention of the other one, who starts coming towards the killed companion. Shoot him also into the head. As soon as the third one appears and he starts waving his pistol around, shoot him quickly to the head to get things right. Walk around the shack and pry the door open.
Inside, there is a trader. From him, you can buy weapons and several useful items, for Byzantine coins. At the moment, you cannot afford the rifle, but it is a good idea to get hoist. Thanks to this, you can zip down the lines. You can return to the trader here at any moment into the game.
As soon as you strike a deal with the trader, leave the shack through the back door, climb up the ladder to the metal plank and zipline straight into the prison.