My stock tank heater is an Allied Precision. It sits on the bottom, 250 watts.
If you don't cover your run then you might think about getting some straw. Spread some on top of the snow. The chickens will walk on the straw. My run is covered on top with a tarp. Then I put clear shower curtains around the sides. That gave the girls a wind free, snow free place to be outside. The pop door could also be open all the time so I didn't have to go out early in the morning to open it (will admit to having a lazy streak). I'm pretty secure as I have electric poultry netting surrounding a large area so didn't worry about securing the coop itself and locking the pop door. Have never had a predator get past the netting yet. I like a lot of ventilation in my coop.
I had a house sitter last winter as we went south for the winter. I was trying to make things as easy as possible for him. That's why I came up with using the larger tote rather than a bucket for water. It didn't need filled as often as a bucket. Being semi transparent meant that it was easy to tell when it needed filled. We're spending this winter in Montana (my first time) this year. I'm having a frost free faucet put in so that I can connect a hose and water everyone. The fewer times I have to be out in the cold the better. I'm not used to the cold.
Since this is your first winter, make sure you have LOTS of ventilation. I have 2 3 foot by 1 foot hardware cloth openings just under the eaves. I also have a 2 foot by 2 foot hardware cloth opening in the back of the coop where the house blocks any wind getting into the coop. And, as I said earlier, the pop door is open year round.