We had a Fafco 4 by 20 water heater for a smaller (5.3' wide x 8.5' long x 2.13' deep, rectangular ) pool and it worked great, got it hot enough for jazuzzi time for parents in the evening after a hot day. We upgraded to a larger pool round pool (15 feet x 48" deep) and it still worked great, though we upgraded pools at the end of the season. Thinking about getting another water heater for the larger pool, as the parents like it warm.
So, definitely get a water heater, they make pools livable in the Washington area. Also, We used 2" foam pink board insulation under our pool and use a solar cover and a debris cover on the pool at night. I am looking to see if there is another way to keep more of the pool heat in at night. It gets cool at night in the summer, so there is a lot of heat loss out the top of the pool.
Good luck!