No comment on the suspensory issue, but for the most part I don't worry about mud too much. If my guy is doing fine at the walk and trot we'll canter a little, I just am aware of the footing (no small circles, no flying changes, etc.)
With horses that I know are clumsy I am more cautious. I know it seems too careful since all our horses live outside and can handle mud, but I was riding a fat mare in the mud who swapped out behind and slipped and fell down. We were both fine but I am definitely more careful with certain horses than others.
A horse recovering from a suspensory that's only cleared to walk with a little trot? You bet I'd be a basket case over having to ride through mud that's slippery and/or more than a couple inches deep! That's asking for a setback. Talk to your vet about this, and be sure to express your concerns re: keeping your horse fit and keeping her energy levels in check (if she gets wild and busts a big buck or bolts and gets loose, you're going to have trouble). If you must go ahead and ride through the mud, ask your vet about wrapping options (If you are a confident and skilled wrapper, you could go for Equifit exercise bandages or Saratoga wraps or something. Obviously, if these are applied wrong, they'll do more harm than good.).
MORE muddy laundry, mare?! But I thought I just washed everything...
I'm not worried about a little mud unless I have a horse that is clutzy. However a horse rehabbing I am paranoid about. The mare I gave away recently had a tendon injury and I constantly checked her legs! I'm paranoid about my new guy even though he has clean legs. I don't want to go through a rehab again and a little mud is a good way to do it if they slip wrong.
I was totally fine with the situation you're describing, right until you got to the rehabbing part. I used to ride in outdoor, hogsfuel rings that were definitely mucky without much concern. Careful in the corners and nothing fancy obviously, but I figured the horses romped in muddy turnout so they could work in it too.
I'd still probably feel that way with my pony if he was in work, he's sure footed and just a little trucker. But I got my other horse just as he was starting suspensory rehab and I would never dream of riding him in the mud because of it. He's now almost a year out of rehab, and doing great, but I still wouldn't consider riding in anything I deemed muddy or even questionable. I actually take the long way down the road instead of walking through some boggy hogsfuel, which most don't have a second thought about, and some have been known to trot and even canter through...
Don't screw up your rehab, that's all I can say. It's not worth it.
I worry about deep mud more than slippery mud. Yes, horses can handle a little mud, but changeable footing can be dangerous. Imagine you are jogging along on solid ground and all of a sudden you stepped in deep or slippery footing...If you knew it was there you could prepare for the change. But if you were suprised, you could seriously hurt yourself.
I've rehabbed a suspensory. You could not get me near the mud you are describing even if you were chasing me and the horse with a lit torch. Even now, several years after that rehab, I would probably stay away from it (I might walk through it).
I would not trot in mud with a recovering suspensory injury. What about walking for a longer length of time instead? Walking in the mud should be harder on the horse, so you might find that a longer walk in the mud is both safe and allows the crazies to come out if you walk for long enough. Maybe try walking over some ground poles for a gentle stretch?