Need opinions on hiking shoes.

The end of this month I plan to hike from the 8,200' base elevation of a ski resort to an elevation of about 11,400' and back down. The length of the round trip walk will be about 18,000' (9,000' X2). The entire distance of the hike will be groomed ski trail. Some terrain will be steep going up and coming down, but no rock climbing or anything like that. It'll be just my wife and me. Not a group thing where I have to keep up with people.

I have a pair of training shoes for running that I am inclined to use for the hike. But having never tried this kind of hike, wonder if I will regret wearing running instead of hiking shoes. I'm cheap, so if there is no material gain with hiking shoes, I'll take a pass on spending the money. On the other hand, if it makes the outing more enjoyable and help prevent ankle or foot injury, then I'll spend the money.

Some of you guys are pretty experienced with the outdoors, so please let me know your thoughts on this. If you think a pair of hiking shoes is the way to go, please tell me what to look for or avoid in a shoe.

My wife already has a pair of hiking shoes. Our destination is Beaver Creek's Birds of Prey downhill course.

Thanks. - Deerfield