About a decade ago they were available. If they are still available who makes them now?
I like to walk ten minutes of every hour to give the horse a break, boots tend not to last under that treatment.
Mountain Horse makes some riding sneakers. I have the Ariat Terrain boots - I think you could run in them for the amount of time you’re talking about.
Brooks Adrenaline. Designed to prevent canting and to keep your foot heel-toe roll dead straight for cross country and mountain marathon running. Fits easily into the endurance stirrups, or a safety stirrup. Light, airy, with a rebounding sole that keeps your foot “fresh” and happy for miles and miles and miles and miles and miles…
They are true trail running shoes. I’ve been using them for endurance riding for over 10 years. Best thing I ever put on my feet. 
I also have the Ariat Terrain boots. I find they feel a little weird in the saddle, but they’re comfy enough that I wear them everywhere else. They’ve gotten nearly daily wear for almost a year, and the sole is now starting to separate at the toe. Considering I do construction work in them, I think they were a good buy.
My Ariat terrains did not hold up very well. Had holes in the front behind the toes within a few months. I have a pair of Avias that have lasted for almost 3 years. They have memory foam insoles and are light weight. Very comfy for walking, riding, and a little running. I think I got them on sale at Kohls for $35. I also have a pair of C9 by Champion from Target. I got them in the boys section for $23 and they are actually very comfy. Only had them a couple of weeks so I’ll see how they hold up. If you don’t really need the heel like the terrains have, I would go try on regular sneakers.Good Luck!!
http://www.valleyvet.com/ct_detail.html?pgguid=30e074bb-7b6a-11d5-a192-00b0d0204ae5
I really like these. Super comfortable and last a long time. I ride, do the barn I work at and go hiking with these.
Although, the waterproof portion doesn’t last too long.
But great price and free shipping.
I have a pair of Ariat Terrains that I purchased 3 or 4 years ago that I am just now needing to get replaced. I will be replacing them with another pair of the same. They are the most comfortable boots I have ever had for riding or walking.
I ride in Ariat Terrains. They’re GREAT.
Not sneakers - but the Twisted X all rounds are VERY comfy!!!
I have several pairs of Montrail trail running sneakers. Very similar description to gothedistance above. I love them!
Another Terrain fan here… first pair still going strong after 4 years. (Key is to keep conditioned… love Passier Ledersbalsam for 'em). They’re wider than the new pair, so I keep the old pair for winter time when I need thicker stocks.
New pair just as comfy for riding, walking, hiking, barn work, etc.
my ariat terrains fell apart after only three months of light use. Would not recommend. I have a pair of the Mountain Horse High riders that are wonderfully comfortable for both riding and walking- which I found out once when the horse went lame and we had to hike back a really long way.
