To estimate the cost difference you need to estimate how much nat gas you would use in a typical winter and use this to calculate its cost from the local utility. You might be able to use the gallons of propane used each year, convert the gallons to BTUs, and convert BTUs to whatever unit the utility sells gas in. I also believe nat gas should be less expensive than propane, especially if you're paying $5.80/gallon.
Another cost to consider if you want to convert to natural gas is that all your propane burning appliances (furnace, water heater, generator, stove/oven) will need to also be converted to natural gas, and some appliances may not be able to be converted due to age or design.