I think I probably approach it from lots of different angles at once. If a horse is worried about something, I have to take that into account. I honestly don't know if there's a bear in those woods, but he really does know - or thinks he does. It can be a real life-and-death fear situation for him. So, I let him stop and look. But not for long. Now if he refuses to walk on quietly, then you have to make his 'standing still' option a lot more work, so that walking on quietly begins to look like a real good deal. When he's standing still, you put his feet to work, backing up, disengaging the hindquarters, moving him sideways ... all these are tools you can be learning if you haven't yet, and when you've got them you'll have a whole lot more confidence with getting him moving again.
Aside from that, I don't think you've handled it badly (apart from the feeling bad and bursting into tears bit - don't do that, it makes me sad). I always get off rather than get into danger - no problem with that. And ending it when the horse gives you a little of the correct response - that's good too.
One thing you could consider for days like this - days when he's for one reason or another, stiff scared and tense - is go for a 'goal free' ride. DOn't set out with an idea of getting to some place or another. Simply ride him out a hundred yards, or less, and start to play. Play at softeness and suppleness, play at tiny bendy circles, play at leg yielding, find a nice gentle little slope and do your bendy circles up and down the slope focus on staying perfectly balanced on every part of it .. take his mind off 'the Big Spooky Thing' ahead, in other words, and occupy him with doing something else entirely.
BTW, it's a myth that out and return rides make for nappy horses. Same myth that feeding treats by hand makes horses bite. Bad training makes both situations worse, but with consistent training you can feed treats, and stop a ride wherever you feel like it and turn for home.