My horse does this sometimes, just turn them, their momentum usually returns and they will be more willing to go forward:)
My horse clover used to do it and I would tap her on her shoulder with my hand and she would start to walk forward and now she stop
What I would do is turn him in a small circle because then he will have to move and then just keep walking
I don't know how to fix the problem when he is walking but when you are riding, try to feel your horse and if he is slowing down before he stops, give him a sign to go faster. My horse does this also. If he stops suddenly, then you might be the one who is the problem (I don't mean any offense by that statement) Your horse might have misunderstood your sign and stopped. If you have a trainer I would talk to him/her about it also.
Hope this helped!
Make him back up a few steps and then ask him to walk again. Repeat if he doesn't move still. I found this works best because most horses hate to back so this is very affective
Hmm my horse does this sometimes when walking over simple little ground poles aha but basically all I do is just kick him until he moves.
So when riding him justice a lot of leg and then if he doesn't listen then kick him until he listens or pull his head and make him to a tiny circle to get him moving.
And on the ground hmm maybe carry some treats with you and when he stops let him smell the treat, but don't give it to him, when you get to the cross ties or where ever you need to bring him then you can give him the treat. Like a reward for going where he needs to go
His surroundings dont bother him. You could stay his stubborn, he also does this when I ride him, I will be walking him to cool him down and he stops and refuses to walk??!