I guess I take for granted that the trails I ride are a freakin' mud-hole for much of the year. The horses just get used to walking through mud and standing water so it doesn't phase them at all.
I never really appreciated it until I went on a ride in the Big South Fork area of Tennessee a few years ago and many of the other riders were having trouble getting their horses to go through puddles. The horses were hopping over them, or skirting around them - often scraping their riders' legs on trees just to avoid the big, bad puddles.
Our horses just plodded right through like it was no big deal.
I'd be careful about dismounting at a puddle or ditch-crossing to try to hand-lead your horse, depending on the terrain. I know people who have tried it - the horse spooked at the water and jumped the ditch anyway AND knocked the person down and stepped on them in the process.
Take your time when you get to that obstacle, and be sure you're not the one getting "nervous" about it. That nervousness can travel right down the reins, the horse picks up on it and thinks that this must be a really legitimate thing to worry about.
Do you have a trail buddy who can ride ahead of you, whose horse will walk calmly through the obstacle? That can be a big help to boost your own horse's confidence.