How do I stop my horses from doing this?

I have two horses and just moved last month to my own acreage, and brought my horses. there is pipe fencing around the house, and for the past 3 or so weeks they have been reaching under to get the grass on the lawn. The pipe only has one bar across the top. I will walk out and they will be on their knees ( =O!!!!!!!!!!) reaching farther out for grass. They go back and forth so they have completely rubbed their manes out in one spot :'( I cut my mares mane because it was already ugly, but my gelding has a long flowing mane and I would cry if I have to chop it off. How do I stop my horses from doing this so I can save their manes? I can't add more pip to the fence because it is to expensive. I need something that won't break the bank but work effectively. Help!!!