Any horse can walk with it's head level-headed. The horse has to be relaxed and comfortable. All horses walking along a field usually walk relaxed with their head low and down.
There are many ways to do this. Watch some videos of trainers who focus on keeping the horse calm, when they are calm, their heads will always be level with their spine. And Inverted horse is never calm and relaxed, and never can be until his neck lowers. I like how Chris Irwin explains how a horse stays calm, and how you can get him to have a level head naturally. You can watch his free video clips on www.statelinetack.com