https://horsefable.com/horse/1899738

I adopted her from rescue back in February and as you can see, she does get levels exp but because I, solely, have one tab dedicated to Exploring Only, she doesn't get much love. 

So they do, its just much less exp/levels than all the others. 

Pretty much Exploring Hoofbeat Plains should be for horses that don't really do good in anything, I suppose you could say. Personally though, I have rescued/bought horses and simply put them to Explore only, whether or not they are better suited for something else? I cannot say, but at least they are getting used and I've even bought older horses in the past and put them to Explore only and used them until they retired, so you probably shouldn't put your horses that do good in Disciplines/Halters for Explore. Best bet is to use like Foundies/low PS horses. ((Someone may have a differing opinion from me but this is how I do it))

They do, my explore only horses are level 15, 11 and 8. However, I also only use low BS/PS horses and save my good discipline horses for showing. I also explore elderly horses that I am done breeding until they retire