Based on the reports of the fall fishing on the Red River this fall, early ice should be very good on the river and the lake. I personally have not fished in December, but doing some research and networking I have learned that a great fall bite typically leads to a great early ice bite.
IF you fish the Red River, I would suggest staying anywhere in Selkirk that has good lighting. Several hotels downtown (Selkirk Inn & Conference Centre) that are a option and a short drive down the EOM (end of main) road, where fishing is done.
If the lake has good fishable ice then accessing the west side of the lake on access, such as Chalet Beach is popular.
Lodging is the hardest to find come March, early ice you should have no problem finding a hotel. Unfortunately there is no resorts to stay at or places on the lake unless you happen to stumble on a cabin for rent.
From the hotels in Selkirk to the river you should be able to get to the fishing spot in 20-30 min, to the lake from the hotel you would be pushing 45 min.