You could always have an increased winter rate and reg summer rate. Or offer the $250 rate for a longer than month to month contract to incentivize long term boarders.
Boarding at a barn over winter with an indoor is always going to attract people seasonally. Heck, where I'm at some people have their own pastures/ facilities but still choose to board in winter so that they can ride more. In the summer the barn makes more profit off of lessons and activities, which offsets the reduced boarders. They know this and market themselves that way.
I don't think your boarders were trying to take advantage of you. They paid your rate and met the contract terms, if you don't feel it adequately covers expenses for short term boarders then you should increase it. For the financially strapped, You could offer to let them go to a self care model for a reduced cost. Self care runs $180 where I'm at. You keep good boarders, less work for you, they save money but have to provide all of their own feed and do the work. The key is to figure out what your profit margin is and try to maintain that margin for both self and full care scenarios.
People who care about their horses will pay for higher quality service and care. Regardless of the area you are in. But you need to present and market yourself as a high quality facility and differentiate your barn from those with lesser offerings/standards. If people are shopping around for price, educate them on the quality and care they get at your place and provide them with questions they should ask when looking at boarding facilities... they'll find out on their own that yours is the better option and be able to make an informed decision.