My cousin and I managed to calculate 15 minutes. 

Personally, I still hope it will either be removed or adjusted. There wasnt one before so I see no point in a cooldown now and it also doesnt make sense to have cooldown just to see what the horse is and then decide not to go after it.

That and 15 minutes is a bit much. 

Yep 15 minutes. I tracked it with my Fitbit recently actually. I believe I checked the Hoofbeat Plains map, every 5 minutes, give or take. I last remember telling Maki, my cousin, 10 or 12 minutes and I STILL couldn't approach one. My stopwatch was winding down to about 14mins and 30 seconds, when I found a wild, I decided to sit and wait out those last 30 seconds before hitting capture, purely out of curiosity, and it was able to let me capture it once it was at 15 minutes with a few seconds over for me to react to stop the stopwatch on my Fitbit.

I remember when it came out, I said I found a wild, tried to capture it and after that, I ran into 6 others but could not capture and brought up it would be nice to see a timer to see how much time is left but after finding out it's 15 minutes? That's a bit ridiculous.

I think there was always a 15 minute cooldown but when wild encounters were random events the cooldown worked in the background so you didn't run into any horses during that time. The difference now is that the cooldown is still there but Explore allows you to run into horses before the cooldown is finished. I think 15 minutes is a reasonable cooldown if you captured a wild horse but is too long for those you shoo or who run away. Maybe a 5 minute cooldown for those cases? Also adjusting Explore to prevent you from running into horses during the cooldown period would help a lot; not having an unatainable horse pop up leaves the chance open for finding an item instead.

I have definitely found wilds the old way within 15 minutes of each other

Hmm well it's great that I know that now! Is a bit frustrating, but I guess maybe they don't want the game getting too saturated with wild horses? 

I also definitely found them way sooner than 15 minutes. There were times I would enter my horses old way before Enter All and I would find a wild in between the 10 pages for each horse or a few horses down the line.

A lot and I do mean a lot of the horses I simply shoo but there may be one I really, really want. Least having a timer would be nice to know so this way if I shoo a horse, I can leave Hoofbeat plains and come back periodically to see how much time is left.